Kinetics of polymer translocation through a pore

We theoretically study kinetics of a polymer threading through a pore embedded in a flat membrane. We numerically solve three coupled kinetic equations for the number n(1) of polymer segments in one side of the membrane and expansion factors of the polymer chain in each side of the membrane. We find the time evolution n(1) proportional to t(1/(1+nu)) at late stages and the translocation time tau(t) is scaled as tau(t) proportional to 1+nu) for large number n of the polymer segments, where nu is the effective size exponent of the radius of gyration of the polymer. When the polymer is translocated into a region with a good solvent condition (nu=3/5), we obtain n(1) proportional to t(5/8) and tau(t) proportional to n(8/5).     

What's so special about polymers? A little known organizing principle gives rise to an abundance of polymer phase transitions

We argue that if an organizing principle exists it must have to do with the linear connectivity of the monomers since this feature is what distinguishes polymers from all other materials. We then compare a linear polymer threading a pore in a membrane (PTM) with an equal number of unconnected monomers which are also allowed to transit through a pore in a membrane. The crucial difference between the two cases is that the connected monomers are distinguishable from one another by virtue of their location along the polymer chain whereas the disconnected monomers are indistinguishable. Because of this, the disconnected monomers obey the ideal gas laws while the connected monomers undergo a first-order thermodynamic phase transition! Four other phase transitions occurring in isolated linear polymer molecules are known. They are the helix to random coil (HR) transitions in biological polymers, surface adsorption (SA), polymer collapse (C), and a model of polymerization (P). These five kinds of transitions can be coupled to one another resulting in a sizable number of exactly solvable minimal models of phase transitions. There are also five classes of phase transitions in many polymers systems. The coupling of these 10 classes of transitions to each-other results in a plethora of phases. These in turn provide the basis for the many polymer structures observed in the world about us. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2612–2620, 2006     

Marked differences in volume phase transitions between gel and single molecule in DNA

Volume phase transitions of a DNA gel and a single giant DNA chain caused by spermidine(3+) (SPD(3+)) were investigated. The change in volume for the single DNA (VV(0) approximately 10(-5)) was four orders of magnitude greater than that for the DNA gel ( approximately 10(-1)), while the critical SPD(3+) concentration for the gel (1.8 mM) was one order of magnitude greater than that of the single DNA (0.12-0.25 mM) at the same pH 6.86. We tried to describe mean-field theories with virial expansion, which is valid for the coil-globule transition of a single polymer chain, for the volume phase transitions to explain the reason why such marked differences appeared. Considering the degree of the ordering of Kuhn segments arising from the gel network structure together with the chain length of cross-linked polymer chains, the volume phase transitions were described and then the significant differences were reproduced quantitatively. We concluded that the network structure plays a significant role in the volume phase transition of the gel.     

Surface-induced phase transitions in ultrathin films of block copolymers

We study theoretically the lamellar-disorder-lamellar phase transitions of AB diblock and tetrablock copolymers confined in symmetric slitlike pores where the planar surface discriminatingly adsorbs A segments but repels B segments, mimicking the hydrophobic/hydrophilic effects that have been recently utilized for the fabrication of environmentally responsive "smart" materials. The effects of film thickness, polymer volume fraction, and backbone structure on the surface morphology have been investigated using a polymer density-functional theory. The surface-induced phase transition is manifested itself in a discontinuous switch of microdomains or a jump in the surface density dictated by the competition of surface adsorption and self-aggregation of the block copolymers. The surface-induced first-order phase transition is starkly different from the thickness-induced symmetric-asymmetric or horizontal-vertical transitions in thin films of copolymer melts reported earlier.     

Slippage of a Porphyrin Macrocycle over Threads of Varying Bulkiness: Implications for the Mechanism of Threading Polymers through a Macrocyclic Ring

Threading of a polymer through a macrocyclic ring may occur directly, that is, by finding the end of the polymer chain, or by a process in which the polymer chain first folds and then threads through the macrocyclic ring in a hairpin‐like conformation. We present kinetic and thermodynamic studies on the threading of a macrocyclic porphyrin receptor ( H₂1 ) onto molecular threads that are blocked on one side and are open on the other side. The open side is modified by groups that vary in ease of folding and in bulkiness. Additionally, the threads contain a viologen binding site for the macrocyclic receptor, which is located close to the blocking group. The rates of threading of H₂1 were measured under various conditions, by recording as a function of time the quenching of the fluorescence of the porphyrin, which occurs when receptor H₂1 reaches the viologen binding site. The kinetic data suggest that threading is impossible if the receptor encounters an open side that is sterically encumbered in a similar way as a folded polymer chain. This indicates that threading of polymers through macrocyclic compounds through a folded chain mechanism is unlikely.     

Histogram Monte Carlo simulation on phase transitions in single‐polymer systems

Applying the histogram Monte Carlo simulation method and the bond‐fluctuation model, various phase transitions in single‐polymer systems were investigated. The critical transition temperature (Θ point) in the coil‐globule collapse transition of a macromolecular chain is accurately determined. Finite‐size scaling results near the transition point are verified. The first‐order transition associated with the freezing/crystallization of a polymer at a temperature below the Θ point is also observed. The free energy profiles associated with these two transitions are explicitly computed. Furthermore, the unfolding phase transition associated with stretching a collapsed polymer chain is investigated. The free energy profile associated with the transition is explicitly computed. Results on the energy cumulants and free energy profiles provide direct evidences for the first‐order nature of the unfolding phase transition.     

A theory of spin-Peierls transitions in chains of exchange clusters

A theoretical approach to analysis of magnetic structural phase transitions of chain polymer heterospin complexes is proposed. The approach is based on the model for spin-Peierls phase transition of chain exchange clusters. The type of the phase transition depends on the elastic constant of the chain. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 849–852, April, 2008.     

Transition from Incomplete to Complete Wetting of Solid Surface in Polymer–Solvent System: 3. The Regime of Weak Adsorption

The transition from incomplete to complete wetting occurring near the critical temperature of a two-phase polymer–solvent system at the substrate surface that weakly adsorbs macromolecules was studied using the Cahn–de Gennes model. It was shown that, depending on the force of attraction between the segments and the wall, the energy of interaction between the segments in the surface layer, as well as on the length of chain, the wetting transition can occur as the first- or second-order phase transitions, or as the tricritical wetting transition. Near the temperatures of these transitions, we determined the character of the variations in the difference of the surface concentrations that are established at the boundaries between the substrate and semidilute or dilute polymer solutions, as well as in the difference between the interfacial tensions and of the cosine of contact angles. It was shown that the temperature of each transition varies inversely to the square root of the molecular mass of polymer, and its deviation from the critical temperature is determined by the type of transition. At the first-order transitions at the SP-regime, the deviation is proportional to the energy of attraction between the chain units and the wall and is independent of polymer chain length, whereas at the critical wetting it is proportional to the squared energy of attraction between the segments and the substrate and increases with polymer chain length according to the N ^1/2law. At the considered asymptotic regime, which corresponds to the substrates that weakly attract polymer chain units, the type of the wetting transition can be regulated by varying only the length of polymer chain at the same energy characteristics of a substrate. The possibility of observing the critical wetting transitions using the solutions of high-molecular-mass compounds is discussed.     

Transition from Incomplete to Complete Wetting of Solid Surface in Polymer–Solvent System: 2. The Regime of Strong Adsorption

The transition from incomplete to complete wetting of the solid surface by a semidilute polymer solution coexisting at equilibrium with the very-dilute polymer solution was studied using the Canh–de Gennes theory under the conditions corresponding to the tricritical state of semidilute solution and strong adsorption of the chain units on a substrate. It was established that the wetting transition can occur as the first- or second-order phase transition or as the transition of tricritical wetting depending on the repulsion energy of segments that are on the substrate surface. Near the temperatures of these transitions, the character of the variations in the differences of surface concentrations that are established at the boundaries of the substrate with semidilute and dilute polymer solutions, as well as in the differences of interfacial tensions and the cosine of contact angle were determined. It was shown that the temperature of each of these phase transitions varies in proportion to the surface potential of the substrate and does not depend on the polymer molecular mass. The observed behavior differs essentially from that established near the critical point of a polymer–solvent system.     

Side chain disorder and phase transitions in alkyl-substituted, conjugated oligomers. Relation to side-chain melting in P3ATs

Certain 4,4'-alkyl substituted 2,2'-bithiazole and bithiazole-thiophene oligomers display an endothermic transition in their DSC trace below their respective melting points. Variable-temperature FTIR, MAS-1H NMR, UV-vis spectra, and XRD all indicate that the thermal transition is due to a crystal-crystal phase transition that we have labeled alpha --> beta. FTIR shows a stepwise increase in the concentration of gauche defects at the alpha --> beta transition temperature, but MAS NMR spectra show little increase in the side chain motion until the mp is reached. UV-vis spectra demonstrate that the conjugated main chains remain essentially planar through the alpha --> beta transition, and significant deviations from planarity occur only at higher temperatures, but well below the mp. The close similarity of this behavior to the phase transitions in long chain n-paraffins and the "side-chain melting" phenomenon in poly(3-alkylthiophenes), P3ATs, suggests that the latter may actually be more accurately described as a crystal-crystal phase transition of the crystalline fraction, driven by side chain disorder.     

Two phase transitions of poly(N-isopropylacrylamide) brushes bound to gold nanoparticles

The thermally induced phase transition of the poly(N-isopropylacrylamide) (PNIPAM) brush covalently bound to the surface of the gold nanoparticles was studied using high-sensitivity microcalorimetry. Two types of PNIPAM monolayer protected clusters (MPCs) of gold nanoparticles were employed, denoted as the cumyl- and the cpa-PNIPAM MPCs, bearing either a phenylpropyl end group or a carboxyl end group on each PNIPAM chain, respectively. The PNIPAM chains of both MPCs exhibit two separate transition endotherms; i.e., the first transition with a sharp and narrow endothermic peak occurs at lower temperature, while the second one with a broader peak occurs at higher temperature. With increase of the MPC concentration, the transition temperature corresponding to the first peak only slightly changes but the second transition temperature strongly shifts to lower temperature. The calorimetric enthalpy change in the first transition is much smaller than that in the second transition. The ratio of the calorimetric enthalpy change to the van't Hoff enthalpy change indicates that in the first transition PNIPAM segments show much higher cooperativity than in the second one. The investigation of pH dependence of two-phase transitions further indicates the PNIPAM brush reveals two separate transitions even with a change in interchain/interparticle association. The observations are tentatively rationalized by assuming that the PNIPAM brush can be subdivided into two zones, the inner zone and the outer zone. In the inner zone, the PNIPAM segments are close to the gold surface, densely packed, less hydrated, and undergo the first transition. In the outer zone, on the other hand, the PNIPAM segments are looser and more hydrated, adopt a restricted random coil conformation, and show a phase transition, which is dependent on both concentration of MPC and the chemical nature of the end groups of the PNIPAM chains. Aggregation of the particles, which may also affect the phase transition, is briefly discussed.     

Nucleation-controlled multiphase transitions

Thermodynamics and kinetics of phase transitions in multiphase systems have been discussed. Thermodynamically admissible transitions have been identified and transition kinetics described in terms of the extended Kolmogoroff-Avrami-Evans model. Different combinations of transitions have been described as directed graphs. Graph nodes represented individual phases, graph edges--transitions. Superposition of parallel transitions in various mother phases, simultaneous transition of the same mother phase into different target phases, and successive (chain) transitions have been analyzed. Detailed solutions for a three-phase system consisting of one liquid phase and two polymorphic solid phases have been presented.     

Effect of polymer architecture on self‐diffusion of LC polymers

Two LC side‐group poly(methacrylates) were synthesized, and their melt dynamics were compared with each other and a third, main‐chain side‐group combined LC polymer. A new route was developed for the synthesis of the poly(methacrylate) polymers which readily converts relatively inexpensive perdeuteromethyl methacrylate to other methacrylate monomers. Self‐diffusion data was obtained through the use of forward recoil spectrometry, while modulus and viscosity data were measured using rotational rheometers in oscillatory shear. Diffusion coefficients and complex viscosity were compared to previous experiments on liquid crystal polymers of similar architecture to determine the effect of side‐group interdigitation and chain packing on center of mass movement. The decyl terminated LC side‐group polymer possessed an interdigitated smectic phase and a sharp discontinuity in the self‐diffusion behavior at the clearing transition. In contrast, the self‐diffusion behavior of the methyl terminated LC side‐group polymer, which possessed head‐to‐head side‐group packing, was seemingly unaffected by the smectic–nematic and nematic–isotropic phase transitions. The self‐diffusion coefficients of both polymers were relatively insensitive to the apparent glass transition. The presence of moderately fast sub‐T_g chain motion was supported by rheological measurements that provided further evidence of considerable molecular motion below T_g. The complex phase behavior of the combined main‐chain side‐group polymer heavily influenced both the self‐diffusion and rheological behavior. Differences between the self‐diffusion and viscosity data of the main‐chain side‐group polymer could be interpreted in terms of the defect structure. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 405–414, 1999     

Structure and phase transitions in poly[bis-(2,2,3,3-tetrafluoropropoxy) phosphazene]

The structure and phase transitions in poly[bis-(2,2,3,3-tetrafluoropropoxy)phosphazene] have been studied by differential scanning calorimetry (DSC) and x-ray diffraction. Two crystalline phases and one mesomorphic phase are found, denoted I, II, and III, respectively. These phases convert reversibly one into the other on heating and cooling. The Phase I–Phase II transition occurs in a temperature range from 5 to 30°C whereas the Phase II mesophase (Phase III) transition proceeds above 80°C. Heats of transitions are measured to be about 29.0 J/g and 3.6 J/g, respectively. Crystalline Phase I is characterized by a monoclinic unit cell with the parameters: α = 24.4 Å, b = 9.96 Å, c = 4.96 Å, γ = 123°. The axes of both chains, traversing the unit cell, are directed along the “c” axis, the main chains having cis-trans conformation. Phase I is the common crystalline structure for the main chain and side chains. The structure of Phase II is controlled mainly by packing of the side chains. Transition of Phase II into mesomorphic Phase III is accompanied with distortion of packing of the side chains. Only regular packing of the main chains of macromolecules in the plane perpendicular to their axes exists in Phase III. Mesomorphic phase III is stable up to the degradation temperature of the polymer. A significant effect of stress on the Phase II–III transition in oriented samples was found.     

Coupling of the Polymer Threading a Membrane Transition to the Membrane Adsorption Transition

A polymer molecule threading through a pore in a plane membrane is allowed to adsorb on either or both sides of the membrane. Further, it is confined to the vicinity of the membrane by two plane barriers lying on either side of the membrane. A lattice model of this problem is exactly solvable by matrix techniques. The equilibrium translocation behavior is described as a function of the polymer MW, the membrane adsorption energies, the solution properties, the barrier separations, applied force, and the temperature. The transition is first-order, meaning that small changes in any of these 9 quantities can in the limit of infinite MW, completely translocate the polymer. The work of Park and Sung who used Smoluchowski-like equations to calculate translocation transit times can be generalized by use of the sea-snake model which is relevant to isolated polymer chains in solution. The physics behind the sea-snake model is that if one monomer is pulled into the membrane, the distance the center of mass of the untranslocated portion of the chain moves is MW^−1/2 of the distance between monomer units. This reduces the effective friction coefficient by MW^1/2. It is found for the sea-snake model that the MW dependence of transit times varies as MW^3/2 or MW depending on whether we use a free draining or a non-free draining picture for the polymer.     

无规共聚物熔体结晶的计算机模拟

1956年Flory基于Onsager的思想提出了高分子有序化的"堆积原理",即由于链的非柔顺性导致链构象的空间各向异性,只有有序化排列才能在有限的空间中放入大量的各向异性分子而不必改变其构象,由此发展的平均场格子理论被向列型有序的MonteCarlo模拟所证明。     

Two-state and continuous phase transitions in lipid bilayers A time-resolved X-ray diffraction study

Structural changes associated with transition from one phase to another have been examined in several lipid-water systems using time-resolved X-ray diffraction methods. Two types of transition mechanism can be recognized on the basis of scattering originating from the packing of the hydrocarbon chains. Two-state transitions are characterized by coexistence of the wide-angle scattering patterns of the initial and final phases throughout the transition region. Continuous transitions, on the other hand, take place through a series of intermediate states that are believed to arise from deformation of the hydrocarbon chain lattice as one phase transforms into another. Two-state processes are observed as subgel to liquid crystal transitions, and continuous transformations are typical of subgel to gel phase transitions. Examples of these transition types are presented and other transitions that do not appear to conform to either of these mechanisms are described.     

Two-state and continuous phase transitions in lipid bilayers A time-resolved X-ray diffraction study

Structural changes associated with transition from one phase to another have been examined in several lipid-water systems using time-resolved X-ray diffraction methods. Two types of transition mechanism can be recognized on the basis of scattering originating from the packing of the hydrocarbon chains. Two-state transitions are characterized by coexistence of the wide-angle scattering patterns of the initial and final phases throughout the transition region. Continuous transitions, on the other hand, take place through a series of intermediate states that are believed to arise from deformation of the hydrocarbon chain lattice as one phase transforms into another. Two-state processes are observed as subgel to liquid crystal transitions, and continuous transformations are typical of subgel to gel phase transitions. Examples of these transition types are presented and other transitions that do not appear to conform to either of these mechanisms are described.     

Phase transitions and structural properties of a thermotropic polyester

The phase transition behavior and the structural properties of a thermotropic polyester, poly-(chloro-1,4-phenylene-trans-1,4-cyclohexanedicarboxylate), were studied by differential scanning calorimetry, x-ray diffraction, polarized-light microscopy, and electron microscopy. The polyester shows two first-order transitions in heating, i.e., a crystal-crystal transition and a crystal-liquid-crystal transition at 190–220 and 300–330°C, respectively. The texture in the liquid-crystalline phase is very similar to that of nematic low-molecular-weight materials. Oriented films of the polyester can be obtained from the liquid-crystalline state. Many fibrils occur in a fractured lateral surface of the film. Bandlike structures 50–100 nm wide were observed in surfaces of both oriented and unoriented films. The direction of the polymer chain axis is almost perpendicular to that of band elongation. In the oriented film, the band structures are perpendicular to the direction of orientation.     

Transitions of tethered polymer chains: a simulation study with the bond fluctuation lattice model

A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density-of-states results have been evaluated for interaction parameters spanning the range from good- to poor-solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and two-dimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.