The aim of this paper is two-fold. First, via a phenomenological consideration I show that, equal... more The aim of this paper is two-fold. First, via a phenomenological consideration I show that, equally with the conventional phases (body-centred cubic, hexagonal planar and lamellar), such non-conventional phases as simple cubic, face-centered cubic, well known double gyroid as well as some other phases could be stable in a vicinity of the critical point in the systems undergoing the order-disorder and order-order transition. A general phase diagram indicating the strength of so-called angle dependence of the forth vertex necessary for existence of these non-conventional phases is presented. Next, I demonstrate via a direct Leibler-like microscopic consideration of the ternary ABC block and graft copolymers that these real systems do reveal these nonconventional phases even close to the critical point. In particular, the ternary ABC block copolymers with a long middle block non-selective with respect to both side blocks are especially inclined to form the gyroid phase. A new cubic non-centrosymmetric phase and some other cubic phases are also first predicted to exist as the most stable low temperature phase instead of the lamellar one. Such a phase behavior is suggested to be common for a new class of materials we propose to call amphiphobic since their (macro)molecules consist al least of three mutually incompatible types of monomers.
ABSTRACT The weak segregation theory (WST) of microphase separation in block copolymers (BC) is b... more ABSTRACT The weak segregation theory (WST) of microphase separation in block copolymers (BC) is based on the vision by Landau (1937) and seminal breakthrough by Leibler (1980) into microscopic theory of as well as the Brazovskii-Fredrickson-Helfand (1975, 1987) understanding of the corresponding fluctuation effects. The WST is especially helpful in the situation when one tries to form the well reproducible ordered morphologies, for which purpose they are to be formed as smoothly as possible. Among other new results in this field, I address the following issues: i) non-conventional morphologies and phase transitions in the bulk and confined ternary ABC block copolymers; ii) the BC phase diagram control via their chemical modification involving thermoreversible association between the different blocks; iii) the WST analysis of the non-centrosymmetric lamellar structures in the blends of the ternary and binary BC; and iv) semidulute BC solutions as photonic crystals.
Correlated random copolymers are multiblock copolymers with a rather large polydispersity in the ... more Correlated random copolymers are multiblock copolymers with a rather large polydispersity in the block lengths: the variation in the block length is of the same order of magnitude as the average block length. The phase behavior of a melt of correlated random copolymers is qualitatively different from the phase behavior of regular monodisperse multiblock copolymers. It was already known that the system undergoes a disorder-order transition to a microphase separated state having a crystal symmetry, where the period decreases sharply with decreasing temperature. The fluctuation corrections to the phase diagram are, however, considerable. Near the order-disorder transition the profiles of the ordered phases are strongly fluctuating, giving the profiles an irregular appearance. Even if the blocks in the molecules are long, there is a large increase in the region of stability of the disordered phase. Below the mean-field spinodal this phase is strongly fluctuating as well, giving it the appearance of a microphase separated structure.
A complete classification of possible types of phase diagrams for associating systems of f-functi... more A complete classification of possible types of phase diagrams for associating systems of f-functional monomers capable of forming weak physical gels (thermoreversible infinite networks) is given within two different approaches. Within the Flory approach only critical solution temperatures can be shown to exist in the diagrams. The other approach accounts for the dominant role of the cyclization effects on finite scales, describes the properties of the considered system more precicely (rather than the Flory approach which deals with infinite cycles only), and produces richer phase behavior for the considered systems. Examples of phase diagrams will be discussed.
... USSR 15: 5, 1296, 1973) 7. VI BEKICHEV, Vysokomol. soyed. ... Curve e has two extrema at (vop... more ... USSR 15: 5, 1296, 1973) 7. VI BEKICHEV, Vysokomol. soyed. ... Curve e has two extrema at (vop)l.~=2/3]l--O/Tl~-~P~1 but curve d has a single max-imum at Ivop=~ll--O/Tl~ P~1, the state of unperturbed coils (a=l) being roached at vop=2/311--O/TI. ...
ABSTRACT Using the mesoscale simulation techniques, self-consistent field (SCF) method and dissip... more ABSTRACT Using the mesoscale simulation techniques, self-consistent field (SCF) method and dissipative particle dynamics (DPD), we study microphase separation in the melt of amphiphilic/nonpolar diblock copolymers. It is shown that the phase diagram for the melt of diblock copolymers with an amphiphilic block can be significantly different from that known for the conventional model of a diblock copolymer. In particular, we find that longer nonpolar blocks may be assembled in micelles separated by a matrix of shorter amphiphilic blocks. The physical reason behind this is connected with the surface activity of amphiphilic monomer units, which forces them to be located in the regions of maximum concentration gradient. In the limit of significant amphiphilicity (surface activity), the resulting morphology corresponds to thin channels and slits of amphiphilic units penetrating through the matrix of a major nonpolar component.
The aim of this paper is two-fold. First, via a phenomenological consideration I show that, equal... more The aim of this paper is two-fold. First, via a phenomenological consideration I show that, equally with the conventional phases (body-centred cubic, hexagonal planar and lamellar), such non-conventional phases as simple cubic, face-centered cubic, well known double gyroid as well as some other phases could be stable in a vicinity of the critical point in the systems undergoing the order-disorder and order-order transition. A general phase diagram indicating the strength of so-called angle dependence of the forth vertex necessary for existence of these non-conventional phases is presented. Next, I demonstrate via a direct Leibler-like microscopic consideration of the ternary ABC block and graft copolymers that these real systems do reveal these nonconventional phases even close to the critical point. In particular, the ternary ABC block copolymers with a long middle block non-selective with respect to both side blocks are especially inclined to form the gyroid phase. A new cubic non-centrosymmetric phase and some other cubic phases are also first predicted to exist as the most stable low temperature phase instead of the lamellar one. Such a phase behavior is suggested to be common for a new class of materials we propose to call amphiphobic since their (macro)molecules consist al least of three mutually incompatible types of monomers.
ABSTRACT The weak segregation theory (WST) of microphase separation in block copolymers (BC) is b... more ABSTRACT The weak segregation theory (WST) of microphase separation in block copolymers (BC) is based on the vision by Landau (1937) and seminal breakthrough by Leibler (1980) into microscopic theory of as well as the Brazovskii-Fredrickson-Helfand (1975, 1987) understanding of the corresponding fluctuation effects. The WST is especially helpful in the situation when one tries to form the well reproducible ordered morphologies, for which purpose they are to be formed as smoothly as possible. Among other new results in this field, I address the following issues: i) non-conventional morphologies and phase transitions in the bulk and confined ternary ABC block copolymers; ii) the BC phase diagram control via their chemical modification involving thermoreversible association between the different blocks; iii) the WST analysis of the non-centrosymmetric lamellar structures in the blends of the ternary and binary BC; and iv) semidulute BC solutions as photonic crystals.
Correlated random copolymers are multiblock copolymers with a rather large polydispersity in the ... more Correlated random copolymers are multiblock copolymers with a rather large polydispersity in the block lengths: the variation in the block length is of the same order of magnitude as the average block length. The phase behavior of a melt of correlated random copolymers is qualitatively different from the phase behavior of regular monodisperse multiblock copolymers. It was already known that the system undergoes a disorder-order transition to a microphase separated state having a crystal symmetry, where the period decreases sharply with decreasing temperature. The fluctuation corrections to the phase diagram are, however, considerable. Near the order-disorder transition the profiles of the ordered phases are strongly fluctuating, giving the profiles an irregular appearance. Even if the blocks in the molecules are long, there is a large increase in the region of stability of the disordered phase. Below the mean-field spinodal this phase is strongly fluctuating as well, giving it the appearance of a microphase separated structure.
A complete classification of possible types of phase diagrams for associating systems of f-functi... more A complete classification of possible types of phase diagrams for associating systems of f-functional monomers capable of forming weak physical gels (thermoreversible infinite networks) is given within two different approaches. Within the Flory approach only critical solution temperatures can be shown to exist in the diagrams. The other approach accounts for the dominant role of the cyclization effects on finite scales, describes the properties of the considered system more precicely (rather than the Flory approach which deals with infinite cycles only), and produces richer phase behavior for the considered systems. Examples of phase diagrams will be discussed.
... USSR 15: 5, 1296, 1973) 7. VI BEKICHEV, Vysokomol. soyed. ... Curve e has two extrema at (vop... more ... USSR 15: 5, 1296, 1973) 7. VI BEKICHEV, Vysokomol. soyed. ... Curve e has two extrema at (vop)l.~=2/3]l--O/Tl~-~P~1 but curve d has a single max-imum at Ivop=~ll--O/Tl~ P~1, the state of unperturbed coils (a=l) being roached at vop=2/311--O/TI. ...
ABSTRACT Using the mesoscale simulation techniques, self-consistent field (SCF) method and dissip... more ABSTRACT Using the mesoscale simulation techniques, self-consistent field (SCF) method and dissipative particle dynamics (DPD), we study microphase separation in the melt of amphiphilic/nonpolar diblock copolymers. It is shown that the phase diagram for the melt of diblock copolymers with an amphiphilic block can be significantly different from that known for the conventional model of a diblock copolymer. In particular, we find that longer nonpolar blocks may be assembled in micelles separated by a matrix of shorter amphiphilic blocks. The physical reason behind this is connected with the surface activity of amphiphilic monomer units, which forces them to be located in the regions of maximum concentration gradient. In the limit of significant amphiphilicity (surface activity), the resulting morphology corresponds to thin channels and slits of amphiphilic units penetrating through the matrix of a major nonpolar component.
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Papers by Igor Erukhimovich