Enhancement of orientation of rigid polymer blocks by incorporating rod–coil block copolymer chains into metal–organic frameworks

Incorporation of polymer chains into metal–organic frameworks (MOFs) is a simple yet efficient method for improving the orientation of the polymer chains. However, due to their rigidity and high molecular weight, many rigid polymer chains are either not easily loaded into MOFs, or not easily aligned within the MOF channels. In this paper, we propose a strategy for enhancing the orientation of rigid blocks by incorporating rod–coil block copolymer chains into MOFs. In this strategy, on the one hand, the rigid blocks have a low molecular weight, so that the steric hindrance effect from the MOF channels could align the rigid blocks more efficiently. On the other hand, because the covalent bonds between the repeat units of the flexible blocks can rotate relatively easily, the steric hindrance effect from the flexible blocks can further help the rigid blocks to be oriented within the MOF channels. In confirmatory simulations, two all‐atom MOF models, [Zn₂(BDC)₂(TED)]_n and [Zn₂(BPDC)₂(TED)]_n (TED = triethylenediamine, BDC = 1,4‐benzenedicarboxylate, BPDC = 4,4′‐biphenyldicarboxylate), are established. With these MOF models, molecular dynamics simulations are performed for the rigid poly(phenylene vinylene) (PPV) chain and the rod–coil block copolymer PPV‐block‐polystyrene (PSt). Further, their respective degrees of orientation (DoOs) are calculated. Within [Zn₂(BDC)₂(TED)]_n and [Zn₂(BPDC)₂(TED)]_n, the DoOs of the rigid PPV blocks of PPV‐block‐PSt are 0.968 and 0.902, respectively, while the DoOs of the rigid PPV chains are 0.865 and 0.711, respectively. These calculation results prove the feasibility of our proposed strategy. © 2019 Society of Chemical Industry     

Shear‐Induced Fabrication of Multiple Parallel Alginate Gel Filaments Using Alginate–Polyethylene Glycol Blend

A rigid assembly of alginates is formed in aqueous media primarily via hydrogen bonding between guluronic units. A flow of aqueous alginate solution in a co‐flow capillary can form alginate gel fibers by contact with Ca²⁺ ions in sheath flow. Mixing with polyols [e.g., polyethylene glycol (PEG)] facilitates the shaping of the alginate assembly because PEG disrupts the assembly of the extended alginate chains to instead form alginate–PEG complexes that exhibit shear‐thinning behavior. The shear‐induced fibrous domains of the globular alginate–PEG complexes can be partitioned by a PEG‐rich phase, resulting in multiple parallel alginate gel filaments when the strong ionic‐field‐induced PEG‐rich phase is adjusted and an alginate–PEG complex phase is used as the aqueous two‐phase separation system.     

氢化松节油体系过量Gibbs自由能及超额焓

利用α-蒎烯-β-蒎烯、α-蒎烯-蒎烷二元体系常压汽液平衡数据,研究氢化松节油体系过量G ibbs自由能及超额焓的关联与计算。由汽液平衡数据求出体系中各组分的活度系数,从而关联得到相应的常压过量G ibbs自由能实验值,结果表明,α-蒎烯-β-蒎烯、α-蒎烯-蒎烷体系对理想溶液呈现较小的正偏差。根据W ilson方程对α-蒎烯-β-蒎烯、α-蒎烯-蒎烷体系的常压过量G ibbs自由能和超额焓进行了计算,计算值与实验值吻合良好,对α-蒎烯-β-蒎烯体系最大超额焓为12.663 1 J/mol,α-蒎烯-蒎烷体系最大超额焓为126.783 7 J/mol。     

Effects of elongational flow on the isotropic-nematic phase transition in freely-jointed rod systems

Summary The effects of polymer chain flexibility and elongational flow field on the isotropic-nematic phase transition are studied by applying a freely-jointed rods model to the Onsager theory. The biphasic region becomes wider and the difference of order parameters between the coexisting phases becomes larger as the flexibility increases. Also, the onset concentration of highly ordered nematic phase becomes lower, the biphasic region narrower and a difference of the order parameters between the coexisting phases smaller as the stretching rate increases. It is shown that there exists a critical point at a sufficiently high stretching rate, which means the existence of a stable monophase above the critical point. We emphasize that there exists not only a unstable biphasic state but also a stable biphasic state in a weakly stretching rate. Thus the order parameter has double values in this stable biphasic region.     

Polarized light scattering studies on the orientational behaviour of liquid crystalline rods immersed in shear flow under the action of an electric rectangular pulse

This paper deals with theoretical treatments for the deformation mechanism of liquid crystal rods by light scattering under H_v polarization condition, when the rods oriented by a shear flow are acted on by a rectangular electric pulse along the direction of the velocity gradient of flow. As in one example, the calculations were carried out to check whether the complicated orientational behaviour of superstructures such as rods and/or spherulites cause significant effect on the profile of H_v light scattering patterns. In the present system, the orientation distribution function of rods was obtained as the solution of the rotational diffusion equation for rotational ellipsoidal particles. In actual calculations for light scattering patterns, the orientational fluctuation with respect to the rod axis is considered to explain the circular type pattern under no external excitation which has been reported in previous experiments. When the orientation functions provide curves showing two peaks by the proper choice of parameters concerning electric field strength and velocity gradient, the corresponding H_v light scattering pattern showed four small dull lobes in the vertical direction indicating the preferential orientation of rods with respect to the shear flow direction in addition to the four sharp large lobes in the horizontal direction indicating the preferential orientation of rods with respect to the electric field direction. This indicates that the H_v light scattering pattern influences the two kinds of orientation of rods.     

Ultra-high-modulus fibers from solution spinning

Ultra-high-modulus fibers such as Du Pont PRD-49 (initial modulus up to ～1000 g/den) and Monsanto X-500 (initial modulus up to ～600 g/den) are spun from solutions. Both polymers are characterized by a high intrinsic rigidity of individual molecular chains and considerable orientation along the fiber axis. The thermodynamics of solution for rigid and semirigid macromolecules is critically reviewed in order to illustrate conditions under which spontaneous formation of highly oriented fibers is expected. In the case of semirigid polymers, the free energy of (random) mixing pure solvent and parallellized polymer may, according to Flory, become positive for some critical value of a “flexibility parameter.” Formation of an ordered phase for semirigid polymers is not, however, observed by lowering temperature or increasing polymer concentration. In the case of rod-like polymers, still according to Flory, at some critical value of polymer concentration (which decreases with the axial ratio of the macromolecule) the isotropic solution of rods undergoes phase separation with formation of a partly ordered solution. This theoretical prediction is satisfactorily verified by data. While Du Pont fibers are spun from this anisotropic solution, Monsanto's X-500 only yields an isotropic solution at room temperature up to the limit of polymer concentration at which crystallization occurs. This inability of X-500 to form anisotropic solutions at the expected critical concentration is attributed to a partial degree of flexibility. Mechanical properties and orientation of fibers spun from the anisotropic solution appear to be superior to those obtained by spinning from isotropic solution, according to Du Pont's results. When a polymer has a partial degree of flexibility, alteration of physico-chemical variables such as solvent type, solvent composition, temperature, and polymer concentration may still be used in order to increase its rigidity. Theoretical arguments and data supporting this contention are discussed. Moreover, alteration of these variables may also be used to alter the crystallization temperature, allowing formation of the anisotropic solution to occur at a high enough polymer concentration. This expectation was verified in the case of X-500. Finally, the all important role of mechanical orientation of solutions is emphasized. According to Hermans, under high enough shear stress, the difference between the isotropic and the anisotropic solution vanishes. In line with these consideration, drawing techniques are particularly useful in order to achieve almost-perfect orientation and theoretical moduli.     

Electric birefringence of cellulose trinitrate in acetone

Electric birefringence studies have been made on a sample of high molecular weight cellulose trinitrate in acetone. The molecule is shown to have only a permanent dipole moment and no significant anisotropic polarisability in this solvent. Both the rotary relaxation times obtained from transient time dependent effects and the amplitudes of the observed birefringence have been analysed in terms of theories for rigid rods, weakly bending rods, worm-like chains and both flexible and stiff random coils. The study indicates that (a) electric birefringence data are sensitive to molecular flexibility and (b) that in this solvent, nitrocellulose of 12% nitrogen content appears to be a stiff, non free draining coil with a dipole moment of the order of a few debye (i.e. ? 10^?29 C m) per monomer unit.     

Sorption and permeation of poly(n-hexyl l-glutamate) — organic solvent systems

To elucidate the permeation mechanism in polypeptide membranes quantitatively, sorption and permeation of organic solvents on and through poly(n-hexyl l-glutamate) (PHeLG) membrane are studied. Sorption isotherms of solvents are monotonous curves characteristic of random mixing of solvent with the side chains of PHeLG. Values obtained for the permeability and diffusion coefficients are explained systematically by the solvent size and affinity to PHeLG. The free volume fraction of PHeLG is larger than that of usual amorphous polymers. Using a membrane prepared by the application of electric field to concentrated PHeLG solution, the influence of orientation of α-helix to the permeation behaviour is examined. While the sorption is affected little by orientation, the permeability and diffusion coefficients decrease systematically with increase of orientation. It is also confirmed that the critical solvent concentration for the orientation in PHeLG-benzene system is about 40 wt %.     

Stress‐induced densification of glassy polymers in the subyield region

Constitutive equations are derived for the viscoelastic response of amorphous glassy polymers in the region of subyield deformations. The model treats an amorphous polymer as a composite material consisting of an ensemble of flow units, immobile holes, and clusters of interstitial free volume moving through a network of long chains to and from voids. Changes in macropressure lead to an increase in the equilibrium concentration of interstitial free volume that, in turn, induces diffusion of free‐volume elements from holes. The mass flow results in dissolution of voids that is observed as time‐dependent densification of a glassy polymer. It is demonstrated that the model correctly predicts stress relaxation and a decrease in the specific volume observed in uniaxial tensile and compressive tests on polycarbonate at room temperature. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 1705–1718, 1999     

粒子在溶液中吸附聚电解质行为及粒子间的相互作用(Ⅰ)模型建立

以自洽场 (CSF)理论为基础 ,综合粒子、溶剂分子和聚合物链节之间的相互作用及聚合物分子链电荷的作用对粒子在溶液中吸附聚合物的影响 ,采用前末端链节决定随机行走模型 (PRDWM)建立了粒子在聚合物溶液中吸附平衡后的粒子表面的链节密度分布的数学模型———链节密度分布函数 ,并通过吸附前后粒子表面自由能的变化建立了吸附聚合物分子链的粒子间的相互作用势能模型     

Aggregate structure change induced by intramolecular helix-coil transition

Self-assembly behavior of poly(γ-benzyl l-glutamate)-graft-poly(ethylene glycol) (PBLG-g-PEG) in ethanol medium was studied by transmission electron microscopy (TEM), scanning electron microscopy (SEM), laser light scattering (LLS), and circular dichroism (CD). The experimental results revealed that the conformation change of the polypeptide graft copolymer exerts marked effect on its self-association behavior. Spindle-like micelles with polypeptide blocks aligned inside the cores are formed in ethanol solution without denaturant acid. When the denaturant acid is added, the rigid α-helix transforms to random coil, resulting in an aggregate structure change from the spindle-like micelle to large compound micelle. For the large compound micelles, the coiled polypeptide chains and PEG blocks pack randomly within the cores, surrounded by the PEG chains outside to stabilize the aggregates.     

T-形分叉槽道纤维悬浮湍流场的数值模拟

The concentration and orientation of fiber in a turbulent T-shaped branching channel flow are investigated numerically. The Reynolds averaged Navier-Stokes equations together with the Reynolds stress turbulent model are solved for the mean flow field and the turbulent kinetic energy. The fluctuating velocities of the fluid are assumed as a random variable with Gaussian distribution whose variance is related to the turbulent kinetic energy. The slender-body theory is used to simulate the fiber motion based on the known mean and fluctuating velocities of the fluid. The results show that at low Reynolds number, fiber concentration is high in the flow separation regions, and fiber orientation throughout the channel is widely distributed with a slight preference of aligning along the horizontal axis. With increasing of Re, the high concentration region disappears, and fiber orientation becomes ho- mogeneous without any preferred direction. At high Reynolds number, fiber concentration increases gradually along the flow direction. The differences in the distribution of concentration and orientation between different fiber aspect ratio are evident only at low Re. Both Re and fiber aspect ratio have small effect on the variance of orientation angle.     

Mathematical modeling and computer simulations of the flow,nematic phase orientation,and heat transfer in thermotropic liquid crystalline polymers

This study includes a mathematical analysis and computer simulations of the injection molding of thermotropic liquid crystalline polymers (LCPs). The particular area of interest is the modeling and numerical evaluation of the orientation of the rigid rods in the nematic phase of LCPs during the filling stage of injection molding. The model is based on a continuum mechanics approach in order to derive the orientation distribution function of rigid rods for different orientation angles. Numerical distributions of average orientation factors are also derived. Computer simulations have been conducted in case studies that investigate the effects of changes in the processing conditions.     

A QUASI-NEWTON ALGORITHM FOR SOLVING MULTIPHASE EQUILIBRIUM FLASH PROBLEMS

A new algorithm has been developed for solving the multicomponent vapor-liquid-liquid equilibrium Mash problem. The algorithm is an extension of the “inside-out” approach proposed by Boston and Britt for the vapor-liquid equilibrium flash problem.

Conventional flash algorithms use temperature, pressure, composition, and phase fraction as the problem independent variables, In the inside-out approach a new set of independent variables is introduced in place of the conventional variables. The new variables are chosen to be as independent as possible of the conventional variables and as free as possible of mutual interaction. Complex phase equilibrium models are used only to generate parameters for a simple equilibrium ratio model. These parameters become the problem independent variables. The Quasi-Newton method of Broyden is employed to promote convergence of these variables.

The algorithm first obtains a solution for the vapor-liquid equilibrium flash. By examining the liquid phase, a heuristic algorithm is employed which quickly locates a two liquid phase composition region of reduced total system free energy when the original liquid is unstable. The solution of the vapor-liquid-liquid equilibrium flash is initiated only when this occurs.

The performance of the algorithm is demonstrated by a number of problems which exhibit varying degrees of nonideality.     

Orientation Kinetics of Screw-Axial Vibration on Glass Fiber Reinforced Polypropylene Composites

Glass fibers oriented with melt flow direction in a vibrational force field perform better than those in steady-state flow fields in a mathematical model of glass fiber orientation in a vibrational force field. From a molecular perspective, the instantaneous impulse and local negative pressure of the macromolecular chains and chain segments generated by vibration accelerate melting, reaching the physicochemical equilibrium. Afterward, the composite samples are scanned with a scanning electronic micrograph to compare reality with statistical analyses of glass fiber orientation, tensile testing, and impact testing. The results indicate that this model enables the prediction of processing and design parameters in the injection molding, from which optimum conditions for polymer design and processing can be discovered.     

A QUASI-NEWTON ALGORITHM FOR SOLVING MULTIPHASE EQUILIBRIUM FLASH PROBLEMS

A new algorithm has been developed for solving the multicomponent vapor-liquid-liquid equilibrium Mash problem. The algorithm is an extension of the “inside-out” approach proposed by Boston and Britt for the vapor-liquid equilibrium flash problem.

Conventional flash algorithms use temperature, pressure, composition, and phase fraction as the problem independent variables, In the inside-out approach a new set of independent variables is introduced in place of the conventional variables. The new variables are chosen to be as independent as possible of the conventional variables and as free as possible of mutual interaction. Complex phase equilibrium models are used only to generate parameters for a simple equilibrium ratio model. These parameters become the problem independent variables. The Quasi-Newton method of Broyden is employed to promote convergence of these variables.

The algorithm first obtains a solution for the vapor-liquid equilibrium flash. By examining the liquid phase, a heuristic algorithm is employed which quickly locates a two liquid phase composition region of reduced total system free energy when the original liquid is unstable. The solution of the vapor-liquid-liquid equilibrium flash is initiated only when this occurs.

The performance of the algorithm is demonstrated by a number of problems which exhibit varying degrees of nonideality.     

Determination of Critical Conditions for Detonation Initiation in a Finite Volume by a Converging Shock Wave

Direct initiation of spherical and cylindrical detonation in a stoichiometric hydrogen–air mixture under normal conditions by a collapsing low-pressure region (cavity) in a space bounded by a rigid shell is considered. The study of the flow with allowance for the actual mechanism of chemical reactions was performed using the finite-difference method based on the Godunov scheme, with a moving computational grid and explicit capturing of the leading shock wave and contact surface. It is established that, for a fixed pressure in the collapsing region and for its radius equal to or exceeding the known critical radius for an unbounded space, there exists a minimum (critical) shell radius, on exceeding which a detonation wave emerges in the flow field under study. In the case of spherical symmetry, the excess internal energy of the spherical layer between the shell and the low-pressure region to be spent on initiation of detonation burning attains a minimum value that far exceeds the critical energy for detonation initiation by a TNT charge in an unbounded space. Key words: discontinuity decay, hydrogen–air mixture, detonation, shock wave, critical initiation energy.     

Block copolymers with a polyvinyl and a polypeptide block: factors governing the folding of the polypeptide chains

AB block copolymers polystyrene-poly(γ-benzyl-l-glutamate) (SG) of various molecular weights and compositions were synthesized and studied by X-ray diffraction and infra-red spectroscopy. They exhibit lamellar mesophases in the solid state and in dioxane concentrated solution. Each sheet of the lamellar structure results from the superposition of two layers: one formed by the polyvinyl chains in a disordered conformation, the other formed by the polypeptide chains in an α-helix conformation arranged in a hexagonal array and generally folded. The comparison of the lamellar structure of copolymers polystyrene-poly(γ-benzyl-l-glutamate) (SG), polybutadiene-poly(γ-benzyl-l-glutamate) (BG) and polystyrene-poly(ε-carbobenzoxy-l-lysine) (SCK) showed that: (1) for the three types of copolymers (copolymers SG or BG or SCK) the number of folds of the polypeptide chains increases with the molecular weight of both the polyvinyl and the polypeptide blocks; (2) for copolymers of fixed molecular weight of the polyvinyl block and fixed degree of polymerization of the polypeptide block the number of folds of the polypeptide chains depends upon the nature of both the polyvinyl and the polypeptide blocks: a polypeptide chain is more folded when it is linked to a polystyrene chain than to a polybutadiene chain but a poly(ε-carbobenzoxy-l-lysine) chain is more rigid than a poly(γ-benzyl-l-glutamate) chain.     

基于随机机会约束规划的复合材料层合板固有频率的铺层角优化设计

对具有随机弹性常数的复合材料层合板的固有频率优化问题进行研究。从单层板的刚度矩阵出发,给出层合板的刚度特性及一阶固有频率最大化的确定性模型,再根据Liu提出的随机机会约束理论,建立了一阶固有频率最大化的Maximax及Minimax的机会约束规划模型,根据试验及随机理论假设弹性常数服从经验分布,给出了弹性常数的经验分布随机数产生及处理随机机会约束的算法,再给出了基于随机模拟的遗传算法求解方法。最后给出了一个具体的复合材料层合矩形板在四边简支边界条件下基频优化的实例,验证了基于随机模拟的遗传算法求解的有效性。     

Melt rheology of segmented polyamides: Effect of block molecular weight

Segmented polyamides, also known as polyether‐ester‐amides, are composed of polyether and polyamide structural units. The rheological behavior of segmented polyamides with respect to the variations in the molecular weight of hard and soft blocks has been studied using a Monsanto Processability Tester. These systems exhibit pseudoplastic flow behavior. The shear viscosity of the segmented polyamides decreases with a decrease in hard block molecular weight up to 1500. However, at low shear rates, the shear viscosity shows marginal change with an increase in soft segment molecular weight. The equilibrium die swell increases with an increase in shear rate, but decreases with increasing temperature. The stress relaxation study of the segmented polyamides reveals that the stress developed during extrusion relaxes exponentially for all the systems. The equilibrium die swell at a fixed temperature and shear rate, the time required to relax a fixed amount of stress and the stress developed after a certain time interval decrease with a decrease in hard block molecular weight up to 1500, but increase with an increase in soft segment molecular weight. The activation energy of the melt flow process increases with the rate of shear in most of the cases. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 1739–1747, 1999