Rigid Macromolecules Research Articles

A monte carlo lattice study of living polymers in a confined geometry

AbstractWe investigate the changes in the average chain length of a solution of semi‐flexible living polymers between two hard repulsive walls as the width of the slit, D, is varied. Two different Monte Carlo models, that of the ‘slithering snake’ and of the ‘independent monomer states’ are employed in order to simulate a polydisperse system of chain molecules confined in a gap which is either closed (with fixed total density), or open and in contact with an external reservoir. It appears that the mean chain length L in a state of equilibrium polymerization depends essentially on the geometry constraints for sufficiently small D. We find that in the case of an open slit the mean length L(D) decreases with D → 0 for flexible chains whereas it grows if the chains are sufficiently stiff. As the width of a closed gap D is decreased, in a three‐dimensional gap L(D) gradually decreases for absolutely flexible chains whereas for semi‐rigid chains it goes through a minimum at D = 2 and then grows again for D = 1. In two dimensions, in a closed strip the average chain length L(D) for both flexible and rigid macromolecules goes through a sharp minimum and then grows steeply in compliance with a predicted divergence for semi‐rigid polymers as D → 0. We attribute the observed discrepancies of our numeric experiments with some recent analytic predictions to the ordering effect of container walls on the polymer solution when chain stiffness and excluded volume interactions are taken into account.

SOLPRO: theory and computer program for the prediction of SOLution PROperties of rigid macromolecules and bioparticles.

Single-valued hydrodynamic coefficients of a rigid particle can be calculated from existing theories and computer programs for either bead models or ellipsoids. Starting from these coefficients, we review the procedures for the calculation of complex solution properties depending on rotational diffusion, such as the decays of electric birefringence and fluorescence anisotropy. We also describe the calculation of the scattering from factor of bead models. The hydrodynamic coefficients and solution properties can be combined to give universal, shape-dependent functions, which were initially intended for ellipsoidal particles, and are extended here for the most general case. We have implemented all three developments in a new computer program. SOLPRO, for calculation of SOLution PROperties, which can be linked to existing software for bead models or ellipsoids.

Influence of polymer conformation on the entrance length in capillary flow

An analysis of the flow of polymer solutions through capillaries by means of pressure profiles was performed in this work. The experiments were carried out with aqueous solutions of flexible and semirigid macromolecules, Polyox and Xanthan respectively. The influence of the macromolecules' conformation on the flow field development is reflected on the different magnitudes of the entry length, being of the order of 60 diameters for the solutions of rigid macromolecules, and of the order of 10 diameters for flexible ones. In addition, the calculated end effects were larger for the rigid macromolecules than for the flexible ones. From these results, it is found that an increase in the entrance length is observed when the pseudoplastic behavior of the polymer solutions is increased.

Transient electric birefringence of colloidal particles immersed in shear flow. Part II. The initial response under the action of a rectangular electric pulse and the behavior at a low alternating electric field

The time-dependent rotational diffusion equation for rigid macromolecules in solution has been approximately solved for two cases in order to extend the electric birefringence technique to streaming-electric birefringence. One is for the initial period through the application of a rectangular electric pulse to the solution immersed in a low shear flow. The purpose of this is expansion of the distribution function into a function series made by the product of the powers of reduced time (= Θt) and hydrodynamic field α ( = G Θ , G: velocity gradient, Θ: rotary diffusion constant) and a surface harmonic P i j cos jφ. The solution for the build-up process at arbitrary electric field strength is found, but is limited to low hydrodynamic fields. The other is for the response when an alternating electric field is applied to the solution in a shear flow. Here, instead of reduced time, the maximum electric field E 0 is chosen as a parameter for the expansion. The expressions for the intensity of the transmitted light through crossed Nicols are derived in two optical systems where the polarizer is set at an angle of 45° and 0° to the direction of the electric field. The results in the former case show that we can determine four parameters, the ratio of velocity gradient to rotary diffusion constant, the axial ratio of a particle, the anisotropy of electric polarizability, and the optical anisotropy factor, from four values observed in two optical systems, namely, two light intensities before applying an electric field and two initial slopes of the build-up after applying an electric field. On the other hand, when a low alternating electric field with extremely high frequency is applied, the build-up of the light intensity in the former case is the same as that of electric birefringence for pure induced dipole orientation. The build-up for the latter optical system is the same as the expression for pure induced dipole orientation of Eq. (38) shown in a previous work.

Modeling membrane filtration of protein and cell suspensions in a vortex flow filtration system

AbstractVortex flow filtration experiments with bovine serum albumin (BSA) solutions and Arthrobacter simplex cell suspensions in a rotary membrane device are modeled in the pressure‐dependent flux and mass‐transfer‐controlled regions. An expression for the concentration‐dependent diffusion coefficients accounting for hydrodynamic and long‐range potential interactions between rigid spherical macromolecules is used for BSA. A shear‐induced diffusion coefficient, strongly concentration‐dependent on the cell concentration, is assumed to describe the diffusion behavior of the cell suspensions. The adjusted model parameters for albumin solutions in the pressure‐dependent region of flux predict the permeation flux behavior for A. Simplex cell suspensions. When the mass‐transfer correlation is calculated using cell diffusion coefficients, based on a volumetric cell fraction that is around half of the average value of the calculated membrane surface fractions, the fluxes are estimated within less than 10.5% relative error. In the mass‐transfer‐controlled region of flux, the volume fractions of cells at the membrane surface are between 0.16 and 0.35, depending on bulk concentration and hydrodynamic conditions.

Rheo‐optical characterization (flow‐birefringence and flow‐dichroism) of the Tobacco Mosaic Virus

AbstractRheo‐optical techniques of determining flow‐birefringence Δn′ and flow‐dichroism Δn″ were employed to investigate a Tobacco Mosaic Virus (TMV) solution under steady‐state and relaxation conditions to obtain further information about molecular dynamics in terms of local and global orientation and flexibility. These effects were investigated in a concentration range of 0,5 g/L ⩽ c ≦ 2,89 g/L, i.e. below and above the critical overlap concentration c* = 2,45 g/L. Although some aggregation was unavoidable it was determined that in the region of c* the dynamic behaviour was not influenced by varying the concentration. Furthermore it was shown that these aggregates naturally appearing in TMV are sensitive to shear force and dissolve at shear rates above 1 s−1. Beyond the critical shear rate this rodlike molecule should show a good agreement of the orientation angles determined through dichroism and birefringence and a constant ratio Δn″/Δn′ which in fact was found. This reveals experimentally that in spite of the sensitivity to different length scales dichroism and birefringence exhibit similar responses to shear forces for rigid and monodisperse macromolecules.

HYDRO: a computer program for the prediction of hydrodynamic properties of macromolecules

HYDRO is a program for the calculation of sedimentation and diffusion coefficients, rotational relaxation times, and intrinsic viscosities of rigid macromolecules of arbitrary shape that are represented by bead models. Actually, HYDRO contains various FORTRAN callable subroutines that can be linked to the user's own programs to account for variability of shape or flexibility. Some hints are given for the use of HYDRO in various situations.

Polarized and depolarized dynamic light scattering study on F-actin in solution: comparison with model calculations

The dynamics of F-actin of different average filament lengths are sudied by polarized and depolarized dynamic light scattering. The experimental data have been compared with model calculations for rigid and semiflexible macromolecules. The polarized DLS spectra follow the predictions for semiflexible rods with a persistence length of (7.5±2.5) μm. Became there is no theory available that includes flexibility in the calculation of the depolarized dynamic structure factor, to a first approximation we used the diffusion coefficients for semiflexible molecules in our rigid-rod model calculations

The initial slope of the transient birefringence of rigid macromolecules under the action of a reversing electric pulse of arbitrary field strength

A solution is presented for the rotational diffusion equation of rigid macromolecules in solution under the action of a reversing electric pulse. The distribution function is expanded into a functional series composed of products tiPj of the power of time (ti) and Legendre polynomial (Pj). The coefficients of the series are then easily obtained up to a higher order of time from the simple recursion formulas. The initial slope of normalized reversing birefringence at an arbitrary field strength is simply expressed by two averages of the first order Legendre polynomial and the second order Legendre polynomial, <P1≳ and <P2≳, initial slope=2Θβ2/γ (1−<P2≳)/<P2≳−6Θβ/γ <P1≳/<P2≳. Furthermore, the initial slope for pure permanent dipole orientation (γ=0) is found to be independent of the electric field. That is, initial slope=−12Θ. On the other hand, the initial slope obtained by neglecting the Brownian motion at high fields is larger by 6Θ. For example, it is equal to −6Θ for pure permanent dipole orientation. This discrepancy is also discussed.

A rheological, optical, and x‐ray study of the relaxation of orientation of nematic PBZT

AbstractThe ultimate properties of liquid crystalline polymers depend upon the achievement of high orientation, usually by means of flow fields. The properties are limited by disorientation which can occur before the product is solidified. Such cooperative orientation and disorientation phenomena also underlie the complex fluid rheology and product microstructure of these materials. The orientation and subsequent disorientation can be followed dynamically by optical and x‐ray techniques. Normally, monitoring of orientation is possible only by “fast” techniqes, such as birefringence, these are not applicable to opaque and strongly scattering liquid‐crystalline systems. To enable examination of the full dynamic response of concentrated nematic solutions of poly(1,4‐phenylene‐2,6 benzobisthiazole) (PBZT) the Daresbury Synchrotron Radiation Source was used. PBZT is among the most rigid macromolecules and serves as a good model for other materials of its class. The orientation process determined optically and from x‐rays is correlated with fluid rheology and availabel theoretical approaches. During relaxation from near perfect mesogen alignment three principal stages of the disorientation process were identified corresponding to solvent disorientation (first stage of stress relaxation), banding (slow stress relaxation and mesogen disorientation), and finally a very slow banding to polydomain transition. © 1993 John Wiley & Sons, Inc.

Reinforcement of polymers by topological superstructures

The frequently inorganic reinforcement-materials have a diameter of < 1 μm and a length-diameter ratio > 1. They have a compatibilizer on their surface. A theoretic description of the compatibilizers can be made by the mechanics of continuum. The expectations which are placed in a molecular reinforcement via rigid rod macromolecules have not been fulfilled until now. On the other hand the progress with reinforcement via topological overstructures is immense. In the present paper, by means of examples, it is shown that with polymer blends morphological structures can be obtained, which are within 10 2–10 3 nm in the mesoscopic field. Micellar structures are well known in polymer blends and show reinforcements of the matrix polymers. By means of thermotropic rigid rod liquid-crystalline polymers, fibrillated structures with a surprising reinforcement-effect could be obtained. Concerning the example of a blend of TPU and PET, unexpectedly high mechanical properties were found on adding coupling-agents. This could be explained by the crystallite lamellae of the PET which have a reinforcing effect.

Behavior of rigid macromolecules in self-assembly at an interface

Self-assembly (SA) on gold substrates of α-helical poly(γ-benzyl-L-glutamate) [(PBLG); molecular weight ∼20 000 kd] with a disulfide moiety attached at its N-terminus (PBLGSS) was investigated. The SA films were compared with control experiments using unlabeled physisorbed (PS) PBLG and Langmuir–Blodgett (LB) deposited PBLG monolayers. Characterization of the films included angle-dependent x-ray photoelectron spectroscopy, reflection–absorption Fourier transform infrared spectroscopy, ellipsometry, and contact angle measurements. For PBLGSS, a SA monolayer was formed wherein the α-helical conformation was retained and the polypeptides were preferentially bound to gold through the disulfide moiety. This terminal bond to the substrate results in a nonplanar distribution of helix axes (i.e., on average tilted up from the gold surface). This is different from the unlabeled PBLG controls, PS film and LB monolayers, wherein, respectively, less polymer was adsorbed and the helices lie in the plane of the gold substrate. Furthermore, polypeptide aggregation in the solution (e.g., in dichloromethane or 1,4-dioxane) appears to have an influence on the self-assembling behavior of these macromolecules relative to known nonaggregating solvents (N,N-dimethylformamide).

Transport of charged macromolecules in an electric field by a numerical method. 1. Application to a sphere

The discretized integral equation (DIE) method by Youngren and Acrivos (J. Fluid Mech. 1975, 69, 377) is generalized to include the effect of time-independent external forces on the transport of rigid macromolecules undergoing Stokes flow in an incompressible, unbounded fluid. According to Ladyzhenskaya (The Mathematical Theory of Viscous Incompressible Flow; Gordon and Breach: New York, 1963), this is achieved by adding additional terms to the integral equations for the fluid pressure and velocity field in the vicinity of the macromolecule. The generalized DIE method should be useful in modeling electrophoresis and related electrokinetic phenomenon of charged polyions in solution. To verify the method, it is applied to an insulating charged sphere subjected to a constant external electric field in which relaxation of the ion atmosphere from its equilibrium distribution is ignored

Synthesis of rigid dendritic macromolecules: enlarging the repeat unit size as a function of generation, permitting growth to continue

Synthesis of rigid dendritic macromolecules: enlarging the repeat unit size as a function of generation, permitting growth to continue

Brownian dynamics simulation of electrooptical transients for solutions of rigid macromolecules

The overall rotational diffusion of rigid macromolecules in solution under rectangular electric field pulses is simulated by Brownian dynamics. We describe computer programs for the simulation of electrooptical transients without restrictions on molecular parameters or electric field strengths. The programs are used first for the calculation of electrooptical transients of molecules with cylindrical symmetry with induced or permanent dipole moments. The simulated data are consistent with analytical results, valid, e.g., for the limit of zero field strength, but have been extended to ranges, where analytical results are not available. Among the two time constants required for fitting of rise curves for permanent dipoles, the smaller one proves to be almost independent of the electric field strength E, whereas the larger one decreases strongly with increasing E; at high E values the two time constants are very close to each other. By comparison of simulated and experimental transients it is possible to analyze hidden contributions, e.g., of an induced dipole moment in the presence of a dominant permanent moment. The simulations are extended to the case of a molecule without symmetry, tRNA, which is used to characterize the hydrodynamic coupling of translational and rotational motion. We show that in this case the influence of hydrodynamic coupling on the dipole moment, the limiting reduced dichroism and the risetime constants derived from electrooptical experiments is very small (≤10%).

Field-induced anisotropy in concentrated systems of rigid particles and macromolecules

This paper presents experimental results on the use of spectroscopic optical polarimetry to study structure in dense systems of rigid particles and rigid polymer liquid crystals. These measurements probe microstructural anisotropy induced by the application of electric fields in the case of dense suspensions of rigid spheres, or flow fields in the case of polymer liquid crystals. It is demonstrated that conservative linear dichroism can measure moments of the particle pair distribution function in dense suspensions. In liquid crystals, the dichroism is a result of field-induced anisotropy in the defect structure of the material.

The fractal nature of 1-step highly-branched rigid rodlike macromolecules and their gelled-network progenies

Highly branched aromatic polyamides characterized by stiff trifunctional branchpoints connected by rigid rodlike segment are prepared by one-step polycondensation and studied in their pregell and postgel states. It is shown that the nature of the growing one-step rigid aggregates in the pregel state is consistent with the fractal model and that because of of the branchpoint and segmental rigidity and the rather large average length of the segments between branch-points, the rigid one. Step fractals are remarkably porous on the scale of the solvent molecules

Synthesis of the triblock copolymers poly-γ-benzyl- l-glutamate-PMMA-poly-γ-benzyl- l-glutamate and study of their conformation in solution

Using the polymeric initiator PMMA with terminal amino groups the authors have synthesized samples of the triblock copolymer of the ABA type, where A is poly-γ-benzyl- l-glutamate (PBG), B is PMMA. The synthesized polymer constitutes a coil of a flexible polymer to the ends of which are attached the helical sequences of PBG. The MM and the fraction of each component in the copolymer vary. Light scattering, flow birefringence and viscometry have been used to investigate solutions of the synthesized samples in DMFA at 25°C. The composition, MMs, intrinsic viscosities, the radii of inertia, the second varial coefficients and optical anisotropy of the copolymers and their components have been determined. A comparative analysis is made of the dependence of the intrinsic viscosity and optical anisotropy on the molecular mass for the copolymers and PBG homopolymer studied. It is shown that the introduction of a flexible long PMMA spacer into the rigid PBG macromolecule does not change its equilibrium rigidity. A model of the structure of the PBG-PMMA-PBG triblock copolymer is proposed helping to explain the body of experimental data.

Flexible and rigid macromolecules in shear and electric fields

Models for rigid and flexible polymers dissolved at low concentration in a dielectric Newtonian fluid and subjected to shear and electric (or magnetic) fields are developed. The rigid polymers are taken to be a rigid spheroid with high aspect ratio and the flexible chains are considered as an elastic dumb-bell with a nonlinear spring constanl. Specific calculation schemes are developed for transient shear and/or electric fields. Rheo-optical properties such as birefringence and extinction angle are calculated and also interesting components for stress tensor are predicted.

Torque constraints for modeling the behavior of rigid and semirigid macromolecules

This work investigates the rotational dynamics of rigid and partially flexible macromolecules in solution by means of Brownian dynamics simulation techniques. In a previous study by Diaz et al. [J. Chem. Phys. 87, 6021 (1987)] on the rotational correlation functions of rigid models, the effect on rotational dynamics from pure rotations of the model’s elements has been neglected due to the difficulty of introducing rotational constraints in the simulations. We present expressions for rotational constraints in a rigid dimer system, which makes it possible to completely describe the translational, rotational, and coupled translational–rotational motions for interacting spherical Brownian particles by employing the generalized algorithm of Dickinson et al. [J. Chem. Soc. Faraday Trans. 2 81, 591 (1985)]. Theoretical studies indicate, and our simulation calculations confirm, that the pure rotational effects are appreciable. The torque constraint expressions are verified by comparison of the simulation results to the exact analytical results for the rigid dimer system. The torque constraint expressions also allow us to examine the effects of flexibility on the rotational correlation functions for a dimer system.