Continuous self-avoiding walk with application to the description of polymer chains

We develop the continuous self-avoiding walk (CSAW) methodology for investigating temperature dependent thermodynamic properties of finite polymer chains without imposing a lattice. This leads to a new concept: the free energy theta temperature, T(theta)(F), at which the free energy is proportional to chain length. Above T(theta)(F), the polymer chain-solvent mixture leads to a single phase, whereas below T(theta)(F) the polymer solvent system has a positive surface tension with a tendency to phase separation to form a globular phase. For finite chains this coil-globule transition lies above the geometric theta temperature at which the distribution describes a Gaussian coil. CSAW provides the basis for a new approach to predict globular properties of real polymers.     

Polymer‐solvent interactions during phase transition in poly(vinyl methyl eiher)/D2O solutions as studied by NMR methods

The structural‐dynamic changes and polymer‐solvent interactions during temperature‐induced phase transition in poly(vinyl methyl ether) (PVME)/D₂O solutions in a broad range of concentrations (0.1‐30 wt.‐%) were studied by ¹H NMR methods. In the whole concentration range the phase transition is manifested by line broadening (linewidth 350‐500 Hz) of a major part of PVME units, evidently due to the formation of globular‐like structures. Above the LCST transition, the fraction of phase‐separated PVME segments is equal to 0.8±0.1, independent of polymer concentration. While at low concentrations the transition is virtually discontinuous, at high concentrations the transition region is ∼ 3 K broad. Measurements of nonselective and selective ¹H spin‐lattice relaxation times T₁ of solvent (HDO) molecules evidenced that at elevated temperatures, where most PVME forms globular structures, a part of solvent molecules is bound to PVME forming a complex; the lifetime of the bound water (HDO) molecules is ≤2 s.     

Monte Carlo simulations of two-dimensional hard core lattice gases

Monte Carlo simulations are used to study lattice gases of particles with extended hard cores on a two-dimensional square lattice. Exclusions of one and up to five nearest neighbors (NN) are considered. These can be mapped onto hard squares of varying side length, lambda (in lattice units), tilted by some angle with respect to the original lattice. In agreement with earlier studies, the 1NN exclusion undergoes a continuous order-disorder transition in the Ising universality class. Surprisingly, we find that the lattice gas with exclusions of up to second nearest neighbors (2NN) also undergoes a continuous phase transition in the Ising universality class, while the Landau-Lifshitz theory predicts that this transition should be in the universality class of the XY model with cubic anisotropy. The lattice gas of 3NN exclusions is found to undergo a discontinuous order-disorder transition, in agreement with the earlier transfer matrix calculations and the Landau-Lifshitz theory. On the other hand, the gas of 4NN exclusions once again exhibits a continuous phase transition in the Ising universality class-contradicting the predictions of the Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase transition.     

Freezing of parallel hard cubes with rounded edges

The freezing transition in a classical three-dimensional system of rounded hard cubes with fixed, equal orientations is studied by computer simulation and fundamental-measure density functional theory. By switching the rounding parameter s from zero to one, one can smoothly interpolate between cubes with sharp edges and hard spheres. The equilibrium phase diagram of rounded parallel hard cubes is computed as a function of their volume fraction and the rounding parameter s. The second order freezing transition known for oriented cubes at s = 0 is found to be persistent up to s = 0.65. The fluid freezes into a simple-cubic crystal which exhibits a large vacancy concentration. Upon a further increase of s, the continuous freezing is replaced by a first-order transition into either a sheared simple cubic lattice or a deformed face-centered cubic lattice with two possible unit cells: body-centered orthorhombic or base-centered monoclinic. In principle, a system of parallel cubes could be realized in experiments on colloids using advanced synthesis techniques and a combination of external fields.     

The phase diagram of a single polymer chain: New insights from a new simulation method

We present simulation results for the phase behavior of a single chain for a flexible lattice polymer model using the Wang-Landau sampling idea. Applying this new algorithm to the problem of the homopolymer collapse allows us to investigate not only the high temperature coil–globule transition but also an ensuing crystallization at lower temperature. Performing a finite size scaling analysis on the two transitions, we show that they coincide for our model in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil–globule transition. As a consequence, also the many chain phase diagram of this model can be predicted to consist only of gas and crystal phase in the limit of infinite chain length. This behavior is in agreement with findings on the phase behavior of hard-sphere systems with a relatively short-ranged attractive square well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2542–2555, 2006     

Interfacial nonradiative energy transfer in responsive core-shell hydrogel nanoparticles

Fluorescently labeled core-shell latex particles composed mainly of the thermoresponsive polymer poly-N-isopropylacrylamide (p-NIPAm) have been synthesized such that an energy transfer donor (phenanthrene) and an energy transfer acceptor (anthracene) are covalently localized in the core and shell, respectively. When the thermally induced particle deswelling is interrogated by photon correlation spectroscopy (PCS), a continuous (non-first order) phase transition is observed. Conversely, when the nonradiative energy transfer (NRET) efficiency is used to probe the collapse of these same particles, the phase transition event is observed to occur over a much smaller temperature range and approaches first-order (discontinuous) behavior. Furthermore, core-shell particles with differing shell thicknesses display identical phase transition temperatures when PCS is used to monitor the transition, while NRET measurements show a clear increase in collapse temperature as the shell thickness is increased. These apparently contradictory results are discussed in terms of a radial phase coexistence that exists in the microgel particles, which arises from a similarly radial inhomogeneity in the cross-linker concentration. The prospects for the NRET technique as a molecular-scale probe of nanostructured microgels are also discussed.     

Pretilt study of double‐layer alignment film (DLAF)

A novel double‐layer alignment film (DLAF) was developed to obtain greater control of the alignment characteristics of the liquid crystal director. The DLAF consists of a thin fluorinated polymer layer on the top of a rubbed non‐fluorinated, non‐branched polyimide layer (PI 2555). Two types of fluorinated polymer with different chemical structures and wetting behaviour on PI 2555 were chosen, to provide either continuous or discontinuous top layers. The continuous top layer DLAF (DLAF‐1) exhibits an abrupt pretilt transition from planar to homeotropic as the top layer thickness increases. The discontinuous top layer DLAF (DLAF‐2) exhibits a gradual transition where the pretilt correlates with the coverage of fluorinated top layer. These two types of transitions fit with de Gennes' local Frederick's transition and Kwok's inhomogeneous alignment theories, respectively. The abrupt pretilt transition system may be promising for chemical/biosensor applications, whereas the gradual transition system is suitable for pretilt control in LCD devices.     

Formation of intermediate micellar phase between hexagonal and discontinuous cubic liquid crystals in brine/N-acylamino acid surfactant/N-acylamino acid oil system

The phase behavior in the brine/sodium N-dodecanoyl sarcosinate (Sar)/isopropyl N-dodecanoyl sarcosinate (SLIP) system has been investigated by means of phase study, static light scattering, and small-angle X-ray scattering. The liquid crystal phases, hexagonal (H(1)) and discontinuous cubic (I(1)), melt upon the addition of NaCl, which shows the similar effect to the increasing of temperature. The addition of SLIP to the brine/Sar solution at high Sar concentration induces the phase transition from H(1) to I(1) via the isotropic micellar solution (W(m2)). The micellar structure in the W(m2) phase also changes from the wormlike to the globular micelle with SLIP concentration. Adding NaCl reduces the repulsive force between the Sar head groups and simultaneously the space of the solubilized SLIP in the palisade layer, leading SLIP to shift their location further into the micelle core. As a consequence, the hexagonal symmetry breaks into the micelle solution and the liquid crystal order is destabilized entropically.     

A model for transition to the mesomorphic state in poly(methyl methacrylate)

The structural instability of a polymer crystal may be due to the involvement of various lattice vibrations in nonlinear resonance. The condition of this involvement is the prevalence of intramode anharmonicity over intermode interaction. A model of phase transitions in polymers of the PMMA type was constructed. Below transition points, coherent states of orientational vibrations of heavy side pendants are formed. The thermodynamic characteristics of these states were found. The structural instability of the polymer lattice is a second-order phase transition.     

单分子水平高分子相互作用的AFM成像与单分子力谱研究

结合作者近期的研究工作,重点介绍了如何把原子力显微镜(AFM)成像及单分子力谱结合(包括原位结合或者离位结合)起来,研究高分子之间的相互作用.本文涉及生物高分子(主要是核酸-蛋白质体系)以及合成高分子体系(如聚氧乙烯,PEO)的相关研究工作.对于生物高分子体系,主要以长链核酸(如双螺旋DNA及RNA)为探针,首先利用A...     

Normal and Lateral Deformation of Lyotropically Ordered Polymer Brush

Summary: Planar polymer brush formed by semirigid chains of freely jointed rigid segments and immersed into a solvent is considered. Brush collapse induced by deterioration of the solvent quality and its deformation by external normal or lateral force is studied. It is demonstrated that these three different situations can be described in the framework of the common approach. It is shown that the collapse is accompanied by liquid‐crystalline (LC) ordering within the brush. The LC transition can be jump‐like (the first order) or continuous, depending on the segment's aspect ratio and grafting density. Transition point is investigated in detail, the corresponding phase diagrams are calculated. It is shown that the phase diagrams of a normally deformed brush have different structures, with a narrow ‘leg’ in the good solvent region for sparsely grafted brush, with two coexistence regions and a triple point, in addition, for shorter segment length or without these features if the chains are densely grafted. For the laterally deformed brush, phase diagrams have similar structures with a critical point in the good solvent regime.

Polymer brush subjected to deformation by normal (top) and lateral (bottom) external force.     

高分子链坍塌转变动力学过程的动态蒙特卡罗模拟

基于键长涨落格子模型和动态蒙特卡罗模拟方法,引入疏水相互作用,对均聚高分子链坍塌转变动力学过程进行了模拟研究.模拟发现,其坍塌时间呈高斯分布,而平均坍塌时间随淬火深度的变化类似于蛋白质折叠,但难以发现局部最小;另外,平均坍塌时间随链长呈指数形式变化.在其坍塌动力学过程中,高分子链构象先由橄榄球状演变为项链状,进而演变为香肠状,最后形成近球状的熔融球;基于团簇数目、团簇大小和非球面参数等参量,对前人提出的动力学过程四阶段划分进行了更为清晰的界定.     

Phase equilibria of polymer dispersed liquid crystal systems in the presence of an external electrical field

The effect of an external electrical field on phase behaviors is reported for polymer dispersed liquid crystal films of 4′‐pentyl‐4‐biphenylcarbonitrile/poly(methyl methacrylate) binary mixtures with various polymer molecular weights. The experimental results show that increasing the molecular weight of the polymer or the electrical field intensity can give rise to an increase in the phase‐transition temperature and a widening of the binary phase region. The lattice theory, regarding a binary system consisting of a rigid nematic liquid crystal and a random polymer, has been extended to the case in which an external electrical field is present. A comparison of the theoretical predictions with the experimental results has been carried out, and satisfactory agreement has been found. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1898–1906, 2007     

Reversible collapse of brushlike macromolecules in ethanol and water vapours as revealed by real-time scanning force microscopy

Environment-controlled scanning force microscopy allowed us to study adsorption and desorption of single poly(methacrylate)-graft-poly(n-butyl acrylate) brush molecules on mica in real time. The molecules transform reversibly from a two-dimensional, extended wormlike state to a compact globular state. The dynamics of the conformational transition was sufficiently slow in order to allow its observation by scanning force microscope in real time. The reversible transformation is effected by coadsorption of water or ethanol, the latter introduces the collapse. Adsorbing ethanol and water from the vapour atmosphere results in a change of the surface properties of mica, either favouring adsorption or desorption of the graft polymer. When the extended, tightly adsorbed poly(n-butyl acrylate) brush molecules are exposed to ethanol vapour, the macromolecules swell and contract to form compact globules. Exchanging the ethanol vapour to a humid atmosphere caused the molecules to extend again to a wormlike two-dimensional conformation. Coexistence of collapsed and extended strands within the same molecule indicates a single-molecule first-order transition in agreement with observations on Langmuir films previously reported.     

Polymer collapse, protein folding, and the percolation threshold

We study the transition of polymers in the dilute regime from a swollen shape at high temperatures to their low-temperature structures. The polymers are modeled by a single self-avoiding walk (SAW) on a lattice for which l of the monomers (the H monomers) are self-attracting, i.e., if two nonbonded H monomers become nearest neighbors on the lattice they gain energy of interaction (epsilon = -/epsilon/); the second type of monomers, denoted P, are neutral. This HP model was suggested by Lau and Dill (Macromolecules 1989, 22, 3986-3997) to study protein folding, where H and P are the hydrophobic and polar amino acid residues, respectively. The model is simulated on the square and simple cubic (SC) lattices using the scanning method. We show that the ground state and the sharpness of the transition depend on the lattice, the fraction g of the H monomers, as well as on their arrangement along the chain. In particular, if the H monomers are distributed at random and g is larger than the site percolation threshold of the lattice, a collapsed transition is very likely to occur. This conclusion, drawn for the lattice models, is also applicable to proteins where an effective lattice with coordination number between that of the SC lattice and the body centered cubic lattice is defined. Thus, the average fraction of hydrophobic amino acid residues in globular proteins is found to be close to the percolation threshold of the effective lattice.     

Friction and adhesion between C60 single crystal surfaces and AFM tips: effects of the orientational phase transition

We have investigated the nanotribological properties of C60 single crystal (111) and (100) surfaces around its orientational order-disorder phase transition temperature, approximately 260 K, by atomic force microscopy and frictional force microscopy (AFM/FFM) in high vacuum. Results show that for both surfaces across the phase transition temperature, the friction force and the adhesive force between a C60 coated AFM tip and the C60 crystal surfaces exhibit discontinuous behavior. The friction force within the applied external load range in the low temperature phase is significantly larger than that in the high temperature phase, with no obvious change in the slope of the friction force curves (the friction coefficient) in the low and high temperature phases. The abrupt change in friction was found to be caused mainly by the abrupt change in adhesion, which, in turn, can be qualitatively understood through changes in the van der Waals interaction and the short-range Coulomb interaction associated with the structural changes across the phase transition. Compared to most other degrees of freedom, the rotation of C60 molecules was found to have little effect on friction and is an ineffective energy dissipation channel.     

Nuclear spin relaxation in poly(diethylsiloxane)

Earlier work showed that heating causes poly(diethylsiloxane) to undergo a first-order transition from a semicrystalline solid to a more mobile viscous—crystalline material. The latter is composed of two phases and analogies between polymer and liquid crystal morphology and behavior have been made. The viscous—crystalline phase in PDES appears to be unique since the literature is devoid of other documented examples. In this study, spin—lattice and spin—spin relaxation times were measured over a wide temperature range. They show a glass transition at 138°K, a crystal—crystal transition at 206°K, and a transition around 250°K which results from translational motion of the polymer chains with respect to each other. This motion is observed in the amorphous phase at a lower temperature than in the crystalline phase. Translational motion in the crystalline phase is observed on melting of the crystallites. The spin—spin data permitted monitoring of the molecular motions in each phase and the data suggest that these phases exert some influence on the molecular motions of each other. The viscous—crystalline phase in PDES may represent a unique model for studying and understanding “precrystalline” behavior and structure in amorphous solids.     

Heat capacity of a polydiacetylene single crystal from 3 to 300 K

Heat capacities C_p of a polydiacetylene-bis(toluene sulfonate) single crystal and its monomer have been measured in the temperature range from 3 to 300 K. The temperature dependence of C_p for both monomer and polymer crystals differs from that for monoatomic solids. By applying a chain lattice model for a polymer crystal, the temperature dependence of the heat capacity can be described assuming a phonon density of states given by bending and stretching modes of the polymer backbone. With a combination of one-dimensional and three-dimensional elastic continuum approximations, the heat capacity has been calculated and a good fit to the data has been obtained. A small peak in C_p was detected at 161 K for the monomer and at 198 K for the polymer. This may be ascribed to a lower-temperature phase transition in the polydiacetylene crystals evidenced by previous x-ray and spectroscopic measurements.     

Effect of chain stiffness and entanglements on the elastic behavior of end-linked elastomers

The effect of chain stiffness and entanglements on the elastic behavior and microscopic structure of cross-linked polymer networks was studied using Monte Carlo simulations. We investigated the behavior of entangled and entanglement-free networks at various degrees of chain stiffness and densities. Based on previous results that indicated that trapped entanglements prevent strain-induced order-disorder transitions in semiflexible chain networks, we prepared the entangled networks by end-linking the chains in very dilute conditions so as to minimize the extent of trapped entanglements. We also considered the entanglement-free case by using a "diamond" structure. We found that the presence of even a very small amount of trapped entanglements is enough to prevent a discontinuous strain-induced transition to an ordered phase. In these mildly entangled networks, a nematiclike order is eventually attained at high extensions but the elastic response remains continuous and the cross-links remain uniformly distributed through the simulation box. The entanglement-free diamond networks on the other hand show discontinuities in their stress-strain data. Networks at higher densities exhibit a more stable ordered phase and show an unusual staircaselike stress-strain curve. This is the result of a stepwise extension mechanism in which the chains form ordered domains that exclude the cross-links. Extension is achieved by increasing the number of these ordered domains in the strain direction. Cross-links aggregate in the spaces between these ordered domains and form periodic bands. Each vertical upturn in the stress-strain data corresponds to the existence of an integer number of ordered domains. This stepwise elastic behavior is found to be similar to that exhibited by some tough natural materials.