Summary_eng (1136181), страница 9
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Predicted within the theory and conrmed by the MD simulation conformational behavior of the dipolar polymer chain was interpreted in the following way. At the small electrostaticinteraction (small λ), which takes place in the strongly polar solvents or at the high enough temperatures, the contribution of the excluded volume interactions always dominates over the electrostaticcontribution. Hereby, the increase in the counterion diameter leads to the swelling of the polymercoil due to the increase in the steric repulsion of the monomers. However, electrostatic interactionsintensify with the increase in the parameter λ and, starting from certain threshold value, they beginto dominate over the excluded volume interactions, that, in such manner, leads to the collapse ofthe polymer chain.
As a result, the presence of even small dipole moments on the monomers will24lead to its shrinkage. Nevertheless, the growth of the dipole length d is accompanied by the simultaneous growth of the counterion diameter and, as a result, the excluded volume interactions beginto dominate again, leading to the expansion of the polymer chain. It is noted, that the results ofthe theory are in the good agreement with the ndings of the computer simulations.In the conclusion of the Chapter 4 the assumptions of the potential applications of the formulated theoretical model are stated.
It is noted, that the model could be applied to the qualitativedescription of the conformational behavior of the polyzwitterions and weak polyelectrolytes.Chapter 5Part 5.1As is known, electric eld is one of the potential external stimuli on the conformations of themacromolecules in solutions, which are used in practice. The change of the external electric eldstrength could be used, for example, to control the release of the molecules of the drug compound,captured by the polymer coil (globule), serving as the capsule for the targeted delivery.
In the caseof the macromolecules, which monomers carry constant dipole moments or have a large enoughpolarizability, the application of the electric eld may lead to such eects, as electrostriction (deformation of the polymer material in the external eld) and dielectrophoresis (movement of thepolarizable macromolecule in the nonhomogeneous eld).Currently, inuence of the electric eld on the conformational properties was studied in depthwithin the statistical models of the strong polyelectrolytes. Conformational properties of the strongpolyelectrolytes are fairly sensitive to the external electric eld (due to the presence of the ionicgroups on the monomers), that makes them perfect systems for the implementation of the targeteddelivery of the drug compounds or for the creation of the articial muscles.
However, there is awide variety of the so-called dielectric polymers, which monomers possess constant in magnitudedipole moment and/or polarizability, which are also susceptible to the inuence of the electric eld.Though, in comparison with the strong polyelectrolytes, eect of the electric eld on the conformational condition of the macromolecule of the dielectric polymer have to be much weaker. Yet,it has to be noted, that theoretical investigations of the dielectric polymers in the electric eldare not presented in the literature as extensively as the ones for the polyelectrolyte macromoleculesystems. Despite the immense practical importance of the studying of the electric eld inuenceon the conformational state of the dielectric polymer chains in dilute solutions (rst of all, for thepharmacology tasks, related to the targeted delivery of the drug compounds), until quite recentlythere were no attempts of the systematic investigation of this problem using the methods of the statistical physics even at the level of the simplest mean-eld Flory-de Gennes type theory.
Therefore,in the rst part of the Chapter 5 the Flory-de Gennes type theory of the conformational behaviorof the exible polymer chain with the isotropically polarizable monomers in the constant uniformelectric eld in the medium of the liquid-phase solvent is presented.Flexible polymer chain is considered with the polymerization degree N with the isotropicallypolarizable monomers with the polarizability γp , located in the solvent, which is modeled as a continuous dielectric medium with the constant dielectric permittivity ε. It is considered, that polymerchain is in the homogeneous electric eld with the strength E. To describe the conformational behavior of the polymer chain in the external electric eld, the simplest Flory-de Gennes type modelwas formulated, considering the gyration radius of the polymer chain Rg as the single order parameter.
It is also set, that polymer chain on average occupies a volume in space, which can beestimated by the gyration volume Vg = 4πRg3 /3. Thus, the total free energy of the polymer chainis written in the following form:F (Rg ) = Fconf (Rg ) + Fvol (Rg ) + Fel (Rg ),(72)where Fconf (Rg ) is the conformational free energy of the polymer chain, which can be estimatedwith the aid of the following interpolation formula912Fconf (Rg ) = kB T α + 2 ,(73)4α252 = N b2 /6 is the mean-square gyration radius of thewhere α = Rg /R0g is the expansion factor, R0gGaussian polymer chain, b is the Kuhn length of the polymer chain, kB is the Boltzmann constant,T is the absolute temperature; the contribution of the volume interactions to the total free energyis estimated with the use of the virial expansion, truncated at the third order (which is acceptablefor the consideration of not so dense globules) 2N B N 3CFvol (Rg ) = kB T+,(74)VgVg2where B and C are the second and third virial coecients of the monomer-monomer volume interactions, respectively; electrostatic contribution to the free energy is estimated as the free energy ofthe dielectric sphere with the dielectric permittivity εp , inserted into the medium with the dielectricpermittivity ε in the constant uniform electric eldFel (Rg ) = −Vg E 2 3ε (εp − ε)3N εγp E 2,=− 4πγp N8π2ε + εp2 3ε +(75)Vgwhere the dielectric permittivity within the polymer volume εp is estimated within the mean-eldapproximation4πγp Nεp = ε +.(76)VgThen, basing on the minimization of the total free energy, the inuence of the electrostatic eldon the conformational behavior of the polarizable polymer chain in the regimes of good and poorsolvents has been investigated.In the regime of good solvent (B > 0), i.e.
when the polymer chain, in the absence of theexternal electric eld, is in the conformation of the swollen coil, i.e. α 1, the minimization of thefree energy provides the following algebraic equation for the expansion factor!√2πγp2 E 23 6√5α −α=N B+.(77)πb33kB T εAs is seen from the equation (77), the presence of the electric eld leads to the eective increasein the second virial coecient and, consequently, to the additional expansion of the coil. In theregion of the strong enough electric eld near the theta-temperature T ' θ (where B ≈ 0), onecan obtain the following estimation (up to the numerical prefactor) for the gyration radius: Rg /b ∼1/5 3/5γp2 E 2 /kB θεb3N .In the region of the poor solvent (B < 0), when in the absence of the electric eld the polymerchain is in the globular conformation, it is necessary to take into account triple correlations of themonomers, so the minimization of the free energy yields the following estimation for the averagedensity of the globule at weak enough eldsρp =N|B|=−Vg2C6πγp2 E 24 + O(E ).2πγp |B| 2CkB T 1 + 3εC(78)The rst term in the right-hand side of the relation (78) denes the density of the globule at zeroelectric eld.
The second term is the rst term of the expansion in the square over the eld E .It is mentioned that at the further increase of the eld strength, the globule-coil transition of thepolymer chain will take place.Before turning to thepanalysis of the numerical results, the following dimensionless parameterswere introduced: Ẽ = E εb3 /kB T , B̃ = Bb−3 , C̃ = Cb−6 and γ̃p = γp b−3 /ε, so the equation inthe expansion factor is written as:√222πγ̃p Ẽ3 6√ 162C̃α5 − α =N B̃ + (79)√2 + 2 3 .ππ α6 6γ̃3 1 + α3 √Np26Figure 8: Phase diagram of the polarizable polymer chain, plotted in the coordinates α-Ẽ .
Greendashed lines are metastable states; red dashed line is the absolutely unstable states. The data isshown for B̃ = −0.5, C̃ = 2.4, N = 105 .Then, basing on the obtained equation, the conformational behavior of the polymer chain in theelectric eld at dierent polarizabilities of the monomers have been obtained (g. 8). At the smallenough polarizabilities of the monomers, increase in the electric eld leads to the smooth increasein the expansion factor. In that case, at the innite chain length limit (N → ∞) at small enoughpolarizabilities of the monomers, the globule-coil transition of the macromolecule proceeds as thesecond-order phase transition. However, if the polarizability exceeds the certain critical value γ̃c ,the globule-coil transition proceeds abruptly.
It is noted that the globule-coil transition points forma binodal with the critical point.Part 5.2In the previous part of the Chapter 5 within the mean eld Flory-de Gennes type theory it wasestablished that in presence of the polarizability on the monomers of the exible polymer chain, theelectric eld application to the dilute polymer solution always leads to its electrostrictive expansion.In other words, polarization of the macromolecule under the eld leads to the occurrence of theadditional eective repulsion between monomers. The appearance of the electrostrictive expansionof the polymer coil in the constant uniform electric eld makes the next question reasonable: how theelectrostriction will inuence on the polarizable molecules concentration of some target compound(TC) within the dielectric polymer volume? In other words, can one inuence on the number ofTC molecules, captured by the polymer macromolecule, by the change of the electric eld strength?As far as is known, until recently this question has not been theoretically studied in the worldliterature, even at the level of the mean-eld theory.
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