V. A. Benderskii

Determination of rate constants for radical telomerization chain growth and transfer from the molecular-mass distribution of oligomer

The ratio of rate constant for growth and transfer X(n), as a function of the chain length n has been found from the measured molecular-mass distributions of the products of tetrafluoroethylene telomerization in acetone, ethyl acetate, chloroform, and carbon tetrachloride. For all these telogens, the function increases by a factor of 1.5–2.5 in the range of n from 2 to 5, is almost constant for n of 6 to 10, and increases by a factor of 7–10 in the range of n from 12 to 20. This behavior of the function X(n) has been explained in terms of the model of diffusion-controlled propagation and kinetic chain transfer. The model takes into account the change in the diffusion nature of oligomers in the form of rigid rods with an increase in their length. A sharp increase in X(n) occurs when the oligomers that accumulate in the environment of growing macroradical sterically restrict the withdrawal of the forming oligomer to the bulk by an effective solid angle, which decreases with the increasing oligomer length and becomes minimal in the region of formation of colloidal particles.

Dynamics of radiationless transitions in large molecules: 2. Recurrence cycles in population evolution of the initial state

Evolution of the population of the initial state S is due to radiationless transitions into a dense discrete spectrum of intramolecular vibrations {Rn} (reservoir R) and spontaneous decay of S and Rn by virtue of coupling with a continuous spectrum of intermolecular vibrations (reservoir Q). An exact solution to the dynamic problem has been found, which indicates that in contrast to the Fermi approximation, which reproduces only the exponential decay of S, the evolution consists of recurrence cycles such that Loschmidt echo (partial recovery of the population of S via back transitions from Rn) appears in each cycle. The width and number of echo components depend upon average characteristics of the spectrum of R. With an equidistant spectrum and the same coupling constants of S with all R states, the decay of S is exponential in the initial cycle and the number of echo components and echo width increase proportionally to the cycle number in subsequent cycles. The increase in the width causes mixing of the echo components and the transition from regular to quasi-stochastic dynamics. Deformation of the equidistant spectrum leads to nonexponential decay in the initial cycle, an increase in the number of components, and a reduction in the number of cycles with regular dynamics.

Dynamics of radiationless transitions in large molecules: 1. Absorption spectra of adjoin reservoir states

The dynamics of radiationless transitions in large molecules interacting with the surroundings is determined by the dense discrete spectrum of final states {Rn}, close in energy to the initial state s, and by the sets of SR-coupling matrix elements and the decay rate constants of S and {Rn}. It has been shown that the shape and the fine structure of the absorption band of the optical transition from the ground to the initial state S ← S0 makes it possible to find the characteristic function of these three distributions. The transformation of the regular spectrum into the stochastic one has been considered.

Phase transitions in a solution of solvated oligomers

Phase diagrams of oligomer solutions have been constructed within the mean-field approximation. The free energy includes the configuration entropy and the formation free energy of both solvation shells of the oligomers and bonds between them, where this formation free energy depends upon the oligomer-solvent and solvent-solvent bonding energies. The equations for spinodal (phase separation boundary) and percolation threshold (solution-to-gel transition) in the oligomer concentration-temperature coordinates have been found. The model makes it possible to determine the position of phase boundaries by quantum-chemical calculations of these energies and to explain the change in the composition of colloid particles and gel, depending on the solvent. The phase separation region has been predicted to narrow and to be displaced toward higher oligomer concentrations in a series of solvents with progressively increasing intermolecular bond energy.

Study of fluoroalkylsilanes, a new class of amphiphilic oligomers: Determination of end groups and chain length

Radiation-initiated polymerization of tetrafluoroethylene (TFE) in the liquid alkylsilanes Si(CH3)4 (I), C2H5Si(CH3)3 (II), and ClSi(CH3)3 (III) produces fluoroalkylsilane oligomers with the general formula R(C2F4)nX, where X = H or Cl in I, II, and III and R is one of the radicals generated by the abstraction of H from the methyl and ethyl groups in I and II or Cl detachment from III. The nature of R has been determined using an NMR technique, and the molecular mass distribution (MMD) has been found from abundances in anion progressions in mass spectra and from DTG and GPC data. At initial TFE concentrations (C0) changed from 0.4, 1, and 0.13 to 1, 2.7, and 0.7 mol/L in I, II and III, respectively, the average chain length 〈n〉 increases from 4–5 to 10–12 and the MMD changes from the unimodal to the bimodal pattern in which the proportion of oligomers with n < 6 decreases with increasing C0. As 〈n〉 increases and the MMD changes, the homogeneous solution becomes colloidal and then turns into a gel. The colloidal particles are largely composed of long oligomers, and the number of solvent molecules per C2F4 unit decreases with an increase in C0 and is 4–7 in the gel.

Radical polymerization of tetrafluoroethylene in solutions of trimethoxysilanes: Formation of colloidal solution and gel of oligomers

Radical polymerization of tetrafluoroethylene (TFE) in solutions of trimethoxysilanes leads to the formation of fluoroalkoxysilane oligomers and the products of their subsequent hydrolysis and dimerization that occur when methoxyl groups are replaced by hydroxyl groups and Si–O–Si links to bind the oligomers are subsequently formed. The chain length of the oligomers increases with the initial TFE concentration, thereby leading to the formation of colloidal solutions. Colloid particles contain oligomers and solvent molecules, the number of which per TFE unit decreases as the chain length grows to 4–6. Partial replacement of the starting solvents, which are also capable of creating a silicone skeleton during polycondensation, makes it possible to control the number of fluoroalkyl chains attached to this skeleton.

Drying of colloidal solutions of fluoroalkyl oligomers

The change in the supramolecular structure upon drying (solvent removal) of colloidal solutions of fluoroalkyl oligomers at atmospheric pressure has been studied using atomic force microscopy. In an initial colloidal solution, micrometer-sized particles of the dense phase consist of randomly oriented oligomers in the form of rigid rods of a 3–5 nm length forming a porous framework filled with solvent molecules, which solvate the oligomer chains. The drying-induced capillary pressure, which in nanosized pores is of the same order of magnitude as the solvation energy, leads to framework deformation, collapse of the pores, and the formation of lamellar and dendritic structures on a 50–100 nm scale. The ordering of these structures (formation of blocks of parallel oriented fibers typical of a fluoroplastic) increases as the heat-treatment temperature and the drying rate are increased, increasing the roughness of the surface (ratio of real to smooth surface area) and its hydrophobicity.

Differential thermogravimetric curves for a mixture of evaporable and degradable chain oligomers

Since the boiling point of oligomers increases with increasing chain length, differential thermogravimetric (DTG) curves of polymerization products are uniquely related to the molecular mass distribution of the oligomers in the chain length region in which the degradation rate is less than the rate of evaporation. Degradation is manifested by narrow, chain length-invariant peaks of the DTG curves so that they are distinguishable from broad DTG bands due to the evaporation of the mixture of oligomers. The detachment of the terminal groups at a temperature T1 and main chain scission at Td > T1 are accompanied by dimerization of macroradicals, evaporation of the dimers in the T1 < T < Td interval, and appearance of the full degradation peak at T ≈ Td. The pattern of DTG curves based on these concepts has been calculated on the assumption of free convection in the boundary layer and a spatially uniform degradation in the melt. As an example, DTG curves for the products of tetrafluoroethylene polymerization in liquid solutions have been considered.

Model problems in depolymerization kinetics of chain oligomers: 2. Random chain scission

Kinetic equations related to the model of random chain scission (RCS) in the initial oligomer and intermediates (radicals and biradicals) have been solved, and the time dependence of concentrations, the average chain length, and its variance have been found. Despite of the difference in the sequence of formation between the intermediates (sequential reduction of chain length in the model of successive detachment of terminal monomer units and the preferential buildup of short chains in the RCS model), the changes in the average chain length in the two models are similar; i.e., they coincide with an appropriate change of the time scale. In the absence of bimolecular recombination, both the models are ergodic and nonmixing, a property that is due to the equidistant nature of the eigenvalue spectrum. Recombination leads to mixing and transition to equilibrium depolymerization. The change of the mode is determined by the ratio between the bond rupture, recombination, and evaporation rates.

Model problems in depolymerization kinetics of chain oligomers: 1. Successive detachment of monomer units from the chain end

For the successive detachment of monomer units from the end of a macroradical (one of the two main depolymerization mechanisms, of which the other is random chain scission), the time dependence of the monomers concentration, the average chain length, and width of the chain-length distribution of oligomers with allowance for the reverse reactions of monomer attachment to the radicals has been revealed without the use of the quasi-steady state approximation. The conditions under which the chain scission and the monomer evaporation occur at thermal equilibrium have been found.