Intramolecular concentration

Analysis of steady state fluorescence of pdymers containing 1-vinylnaphthalene resulted in the choice of the term f n 1 to describe the intramolecular concentration dependence of the observed excimer characteristics. The same ccmcentration function was thus adopted in the time-resoJved work and produced more satisfactory fits to concentration dependences of functions concerning X and Xj (as plotted in Figs. 26 to 29) than did any other terms descriptive of the chain microccxnposition. 

The box-like cell model of a PE star can be considered as a generalization of a classical mean-field Flory approach, which was first suggested to describe the swelling of a polymer chain in a good solvent [90], The Flory approach estimates the equilibrium dimensions of a macromolecule, as a function of its parameters, by balancing the free energy of intramolecular (repulsive) interactions with the conformational entropy loss of a swollen chain. Within the box-like approximation, the star is characterized by the radius of its corona, R (end-to-end distanee of the arms), or by the average intramolecular concentration of its monomers ... 

Star-branched polymers upon the increase in star concentration, occurs only in the semidilute regime, i.e., when the average polymer concentration in the solution exceeds the intramolecular concentration in an isolated star [24]. 

Erom the summary of the theoretical results presented above, it follows that the intramolecular volume of a star-branched PE, with a sufficiently large number of arms, is essentially electroneutral. That is, the bare charge of a star polymer is neutralized by mobile counterions. These counterions are predominantly retained inside the macroion volume, even if the star is immersed in a dilute salt-free solution. Moreover, if the intrinsic Debye length associated with the intramolecular concentration of entrapped counterions, = l paNis used as an upper estimate for the intramolecular electrostatic screening length, one finds that in the osmotic PE star, p a), the electrostatic interactions are screened at... 

The effect of salt on the conformations of a many-arm (osmotic) PE star becomes important when the salt-controlled bulk Debye screening length, given by (33), becomes smaller than the intrinsic screening length, in a salt-free osmotic PE star. This is also true, equivalently, when the concentration of added salt exceeds the intramolecular concentration of counterions in the osmotic star. Clearly, the local electroneutrality in this case is ensured, and the LEA is applicable for analysis of the PE star conformations on a length scale larger than td. 

Liu, W. J., Bedro, D., Kumar, S. K., Veytsman, B., and Colby, R. H. 2009. Role of distributions of intramolecular concentrations on the dynamics of miscible polymer blends probed by molecular dynamics simulation. Physical Review Letters 103 037801-4. 

When q Rg > 1, concentration fluctuations within single macromolecules dominate the correlation tunction. The calculation ot the light-scattering correlation tunction S q,x) tor a single macromolecule in solution is described in detail in Berne and Pecora. The chain is modeled as shown in Equation 5.10. Intramolecular concentration fluctuations resolve into a set ot modes with characteristic relaxation times that depend on the subchain friction coefficient, the overall radius ot gyration, and the temperature. The correlation txmction can be expressed as ... 

The scaling concept was applied for the analysis of chain conformations and static properties of the semidilute polymer solutions. The unique characteristic length scale in dilute solution imposes a unique characteristic concentration of the solution, which coincides with the intramolecular concentration c in an isolated coil. All the properties of the semidilute solution can be derived from those of the dilute solution by scaling procedure with the aid of proper crossover functions of a single dimensionless variable c/c. These crossover functions are universal, that is, independent of any details of chemical stmcture of the chains, and exhibit power-law asymptotic behavior at c/c 1. 

Solutions of star-branched polymers exhibit typical features that result from the branched topology of the maaomole-cules. In particular, branched polymers are charaderized by smaller dimensions and larger intramolecular concentration of the monomer units, as compared to those of linear polymers with the same degree of polymerization. 

Interestingly, as follows from eqns [58] and [57], average intramolecular concentration of the monomer units in the star... 

The onset of the collapse transition (which corresponds, e.g., to vanishing second virial coefScient of interactions between the stars) is shifted with respect to that for linear polymer of the same degree of polymerization (defined by eqn [54]) toward poor solvent strength conditions. This shift is explained by larger intramolecular concentration in the star polymer close to the 6 point, r=0. 

Eqrration [86] essentially rmderestimates tbe average dimensions of randomly branched polymers and predicts an infinite increase in tbe intramolecular concentration of tbe monomer rmits as a function of N. Tbe effect of tbe intramolecular short-range (excluded-volume) repulsions on the conformations of the randomly branched polymers can be taken into account within the Flory mean-field approach by balancing the conformational entropy losses in the uniformly swollen randomly branched polymer ... 

Intramolecular concentration dependence The study of photophysical phenomena in homopolymers alone precludes variation of one of the most powerful parameters available to a photochemist, namely concentration. The local concentration experienced by the constituent chromophores of a pol3mier may be varied to some extent by altering the thermodynamic compatibility of the solvent and more dramatically by the use of copolymers containing the luminophore of interest and a spectroscopically inactive comonomer. 

It should be stressed that it is important to generate functions descriptive of excimer formation from a given type of chromophore if it is intended that the influence of factors such as chain mobility and comonomer geometry are to be assessed by studying the emission characteristics of a series of copolymers of varying structure. It is not sufficient to merely compare the spectral data obtained from copolymers of equal aromatic content [46]. Furthermore, the intramolecular concentration terms derived from studies under steady state conditions have assumed importance in derivation of rate parameters within the context of one model which has been applied to transient emission data as will be described in section 4. 

In scheme (3), it is envisaged that D, the excimer, is populated from M, by an exciton sampling mechanism M is a chromophore that enjoys a certain degree of kinetic isolation from the normal distribution of quenched excited monomer. The M sites are not unquenched as supposed in the kinetic scheme of Holden et al [18], but suffer an intramolecular concentration dependent quenching that is supposed to originate from energy transfer into the reservoir of M sites. 

Table (II) summarizes the procedures for deriving rate constants from the rate parameters X. resulting from analysis of i (t) according to Equation (6). It should be noted that a measure of the self-consistency of the scheme, the extrapolative procedures and the intramolecular concentration functions adopted is afforded by the fact that each of the derived parameters may be checked through comparison of values obtained by alternative extrapolation approaches.

Implementation of this extrapolation method requires appropriate concentration terms to be adopted to describe the intramolecular concentration dependence of the rate parameters A.. In this context it has been assumed that the variation in aromatic content in the copolymers dominates the variations in photophysical behaviour across the the range of aromatic compositions and that microcompositional terms derived from steady-state analysis of sufficient to characterize the de-... 

Superimposed on these microcompositional effects are those of intramolecular concentration effects revealed in molecular weight effects upon time-resolved emission data [73,90] and the influence of intramolecular chromophore concentration upon the luminescence characteristics of copolymers. The self-consistency of rate-parameter data derived from time-resolved measurements on series of copolymers is good evidence for the assignment (in the copolymers studied to date) of observed decay times as averages representative of chromophore distributions centred on species of the type M, M and D in kinetic scheme (3). 

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