Random Coil Polymers Research Articles

Self-diffusion by giant micelles and random-coil polymers is fundamentally similar

Self-diffusion by giant micelles and random-coil polymers is fundamentally similar

Acid denatured apo-cytochrome c is a random coil: Evidence from small-angle X-ray scattering and dynamic light scattering

The conformation of a denatured protein has been investigated, since the experimental data on the structure of denatured proteins have been incomplete until now. The Stokes' radius R, and the radius of gyration R g of apo-cytochrome c at pH 2.3 have been determined by dynamic light scattering and small-angle γ-ray scattering respectively. The values of these structure parameters, extrapolated to zero protein concentration, are R g = 3.0 nm and R g = 4.6 nm. The ratio R R · R S −1 is a sensitive indicator of the molecular conformation. The ratio of 1.55 obtained by us is typical for a random-coil polymer. The persistence length - the characteristic of the molecular flexibility - was determined to be a = 1.81 nm. Froom this results root-mean-square average end-to-end distance of the molecules <h 2> 1 2 = 11.2 nm and the characteristic ratio < h 2/ n p I p 2 = 8.43, where n p = 104 is the number of amino acid residues and l p the distance between C a-atoms. We obtained a second virial coefficient A 2 = 8.2 · 10 −3 mol cm 3 g −2 . The experimentally determined structure parameters are in approximate agreeement with those predicted by Flory and others for an unpertured, randomly coiled polypeptide. The expansion factor lies between 1.1 and 1.2. In conclusion, we have shown that apo-cytochrome c at pH 2.3 and at low concentration has the conformation of a perturbed random coil with repulsive potentials between the chain segments.

Cooperation in a deep helical energy well

AbstractIn contrast to random coil polymers, polyisocyanates maintain a highly extended helical conformation in solution. This structural characteristic causes unusually large chiral optical properties to arise from copolymerization of tiny proportions of optically active monomer isocyanates with achiral isocyanates or even from stereospecific placement of deuterium in the side chain of poly(n‐hexyl isocyanate). These effects can be understood as phenomenologically related to the optical activity amplification properties of vinyl polymers studied by Pino and his co‐workers and ascribed to breaking the energetic degeneracy of the otherwise equally populated left‐ and right‐handed helical states of the backbone. Statistical thermodynamic calculations, based on this model, and analogous to those carried out earlier on the vinyl polymers, allow matching the temperature and molecular weight dependence of the optical activity in poly((R)‐1‐deuterio‐1‐hexyl isocyanate) to the approximate responsible energy terms.

The concentration dependence of the ‘zero-shear’ specific viscosity for a commercial hydroxyethylmethylcellulose (HEMC) in water at several temperatures

This short paper presents preliminary results on the ‘zero-shear’ specific viscosity η sp 0 of a commercial hydroxyethylmethylcellulose (Tylose MH-4000) in water, at the temperatures 10, 25 and 40·5°C, over a wide range of concentrations. At the two higher temperatures, two regions are found in the plot of log C[ η] 0 against log η sp 0 with a C ∗[η] 0 value of about 2·5. This is consistent with the behaviour of other random-coil polymers. At 10°C however, there is an interesting ‘upward shift’ in this plot in the dilute region. It is suggested that this is related to the different degree of hydration of the oligo(ethyleneoxide) side chains at this temperature.

A hierarchy of models for the dynamics of polymer chains in dilute solution

The dynamics of a hierarchy of sophisticated polymer models described by an interbond potential of quadratic form is derived in the optimized Rouse–Zimm (ORZ) approximation introduced by Bixon and Zwanzig. The resulting quadratic ORZ configurational potential for a generalized rotational isomeric states (RIS) model preserves the maximum of local details and of degree of stiffness compatible with a universal description of polymer dynamics. The present matrix-based RIS–ORZ description has analogies with Allegra’s scalar Fourier approach in terms of the generalized characteristic ratio for chains with periodic boundary conditions. The hierarchy of models amenable to quantitative calculations includes the more popular models used in polymer statistics as the freely jointed and freely rotating chain as well as the more sophisticated models with interdependent rotational states. Comparisons are made in the latter case between the present results and those obtained analytically with the simplifying assumption of a conformationally periodic chain. The relaxation spectra are explicitly calculated for polyethylene, isotactic polystyrene, isotactic polypropylene, and polydimethylsiloxane, which display large differences in stiffness among random coil polymers.

Determination of the flexibility parameter of polymers

Abstract This paper deals with the determination, in theta conditions, of the flexibility parameter λ defined by Kratky-Porod for random-coiled polymers, using three different methods: (a) from hydrodynamic data in θ conditions, (b) by using a new form of extrapolation to zero of the corresponding values for the average molecular weight, and (c) by extrapolation of λ tending to zero. From method (b), values of the interaction parameter, B, were in agreement with those from Stockmayer-Fixman theory. A linear relationship was obtained from (c) by plotting (R2/L)½ versus λ. The slope, h∗, of this plot was found to be related with λθ in the following way: where A1 and A2 are constants, and h is the monomeric unit projection length in terms of the wormlike theory.

Influence of an elongational flow field on random coil and rod-like polymers in solution

The conformational response and spatial arrangement of random coil and rod-like macromolecules in solution was investigated utilizing an opposing jet device. This device is capable of generating a well-defined elongational flow field, which is quite useful for probing intra- and intermolecular interactions of sulphonated polystyrene (random coil) and xanthan (rod-like chain). With regard to the random coil in an aqueous environment, it was determined that its behaviour below the critical overlap concentration ( C∗) follows the anticipated trends as predicted by theory. Above C∗, the elongational behaviour is determined by the intermolecular entanglement structure. However, changes in the ionic strength in these latter solutions reverts behaviour to that observed below C∗. One implication of this finding is briefly discussed. Interestingly, intermolecular interactions dominate the behaviour of rod-like polymers, such as xanthan, below and above C∗. Superimposed on these interactions is the subtle influence of the flow field both outside and along the axis connecting the centre of the jets. These results confirm that the xanthan macromolecule behaves as a liquid crystal at all concentrations investigated, even with relatively large changes in ionic strength.

Molecular weight determination of acrylonitrile polymers by gel permeation chromatography in N,N‐dimethylformamide

AbstractPeculiar elution behavior of the GPC of acrylonitrile polymers was investigated. The peculiarity was considered to be due to some substances which form a supermolecular structure with acrylonitrile polymers to cause a large UV absorption, detectable at 280 nm. The Mark‐Houwink‐Sakurada parameters of acrylonitrile polymers in 0.01M LiBr‐DMF at 60°C, needed for GPC universal calibration, were determined to be K=2.12 × 10−4 and a=0.75. The parameters obtained by us were different from the ones by other investigators, however, these values were reasonable for random coil polymers. The addition of inorganic salt, such as LiBr, in DMF removed the peculiar elution behavior of the GPC. The universal calibration using monodisperse poly(ethylene oxide) standards and the Mark‐Houwink‐Sakurada parameters could be applied for the determination of the molecular weights. The invalidity of the universal calibration for acrylonitrile polymers in DMF containing LiBr, seems to be caused by the difficulty in the determination of the molecular weight of polyacrylonitrile standards by absolute methods, such as light scattering and osmometry.

10] Hydrodynamic characterization of random coil polymers by size exclusion chromatography

This chapter discusses hydrodynamic characterization of random coil polymers by size exclusion chromatography. It also explores some of the problems that have been encountered, and describe current approaches to this goal. As the fundamental process that determines the elution volume of a macromolecule is size exclusion, either occurring in the interior channels of the beads, or at their external surfaces, the chapter prefers term size exclusion chromatography (SEC), but gel permeation chromatography (GPC) and gel filtration chromatography (GFC) are also used to describe the same separation process. This chapter reviews a method of constructing a universal calibration curve that has proven to be quite successful by high polymer chemists, and probably deserves wider use among biochemists working with flexible biopolymers. Finally, the chapter follows by a review to relate elution volumes obtained by SEC to the hydrodynamic and statistical parameters of random coil polymers.

The conformational structure of A-gliadin: Intrinsic viscosities under conditions approaching the native state and under denaturing conditions

The intrinsic viscosity of the wheat storage protein A-gliadin was measured under solvent conditions intended to approach the conditions of protein biosynthesis in the developing endosperm. In studies of intrinsic viscosity, a compromise was sought between solvent conditions that promote unfolding of the A-gliadin polypeptide chain (low pH, denaturing agents) and those that promote aggregation into microfibrils and, eventually, precipitation (neutral salt solutions). The lowest intrinsic viscosity (4.0 ml · g −1) was obtained in 0.01 M NaCl (pH 4), where A-gliadin undergoes aggregation. The intrinsic viscosity, which is in the range of those observed for globular proteins, indicates a compact structure for the A-gliadin aggregates and, possibly, for the A-gliadin subunits that make up the aggregates. The intrinsic viscosity of A-gliadin increased sigmoidally when plotted as a function of guanidine hydrochloride (GuHCl) concentration (pH 5) from 9.5 ml · g −1 in 1 M GuHCl to 18.5 ml · g −1 in 5.9 M. GuHCl with midpoint at about 3.8 M. When the intramolecular disulfide bonds of A-gliadin were reduced and alkylated, the initial viscosity in 1 M GuHCl was about the same as for the intact protein, but the transition occurred earlier (mid-point near 2 M), and the intrinsic viscosity in 5.9 M GuHCl was 29.5 ml · g −1. When A-gliadin was treated as a random-coil polymer under the latter conditions, the intrinsic viscosity corresponded to M r 31 900, in good agreement with results obtained by sodium dodecyl sulfate polyacrylamide gel electrophoresis.

Mesophase formation in lyotropic polymers

The behaviour of polymers for which the mesomorphic property is primarily related to rigidity or partial rigidity of the chain backbone is discussed. The former part of the paper includes an outline of current theories, which describe the phase equilibria of both low-and high-molecular-weight mesogens in the undiluted and diluted states. In the latter part of the paper phase behaviours of rigid and semi-rigid polymers are briefly reviewed. Detailed phase diagrams are considered for the systems poly-γ-benzyl-L-glutamate/dimethylformamide and poly-p-benzamide/dimethylacetamide-LiCl. The correlations between experiments and theory are discussed. The mesomorphic behaviour of cellulose and its derivatives and ternary systems involving two rodlike solutes or mixtures of rodlike and random coiled polymers are also considered. Experimental results provide substantial confirmation for the theoretical predictions of mesophase formation in lyotropic polymers.

Small-angle neutron scattering of polymer solutions

Abstract The angular dependence of the small-angle scattering of concentrated polymer solutions is calculated, using a random coil polymer model consisting of rod-like segments. A Gaussian radial distribution function of the segments is assumed, considering that the local segment density in the solution is almost constant in high concentration. When the segment interaction is weak, the scattering intensity becomes a monotonically decreasing function of the scattering angle. But when the interaction is sufficiently strong, it has a maximum. This maximum point is proportional to the square root of the polymer concentration. This is in agreement with a recent small-angle neutron scattering experiment on polyelectrolyte solutions. Assuming suitable values of the interaction parameters of the segment, a quantitative comparison of the calculated maximum points with the experimental values is made, and from this the segment length and the average end-to-end distance of this polyelectrolyte molecule are determined.

Separation of macromolecules by reversed-phase high-performance liquid chromatography : Pore-size and surface-area effects for polystyrene samples of varying molecular weight

The separation of polystyrenes of varying molecular weight by reversed-phase high-performance liquid chromatography has been studied, using both isocratic and gradient elution with tetrahydrofuran—water mobile phases. Bonded-phase Zorbax® and Zipax® particles (C 18-silica) of different pore-diameters were used: 6, 15, 30 and 100 nm. The results confirm that the normal exclusion of high-molecular-weight random-coil polymers from small pores ( e.g., 6 nm) has little effect on the reversed-phase retention process. That is, effectively all of the bonded phase within the particle is available for interaction with these sample molecules. Quantitative relationships are derived which permit the interpretation of the present data and its extrapolation for the optimization of reversed-phase separations of polystyrene mixtures.

Prediction of sedimentation coefficients of random coil polymers

AbstractThe concentration dependence of the radius of gyration and the equivalent hydrodynamic radius of polymers in solution is described well by a model developed in earlier work. The calculated hydrodynamic volumes of solvated polymers are combined with the statistical mechanical calculations of Burgers for hard spheres to predict sedimentation coefficients at finite concentrations. The predicted values are in good agreement with experimental results.

Viscosity-molecular weight relationships, intrinsic chain flexibility, and dynamic solution properties of guar galactomannan

Molecular theories of the viscosity of dilute and more concentrated solutions of random-coil polymers have been applied to five molecular-weight fractions of guar galactomannan. The variation in intrinsic viscosity ([η]; dL.g −1) with molecular weight (M r) followed the relationship [η] = 3.8 × 10 −4) M r 0.723, consistent with random-coil behaviour. The intrinsic stiffness of the galactomannan backbone was estimated by evaluating the “characteristic ratio” C ∝, which is ∼ 12.6 and agrees well with results for carboxymethylcellulose, which has a closely similar, β-(1→4)-linked polymer backbone. At intermediate concentrations (c), up to specific viscosities of ∼ 10, η sp was proportional to c 1.3, while at higher concentrations, η sp was ∼c 5.1. This exponent is higher than is usually observed for polymers interacting purely by physical entanglement, and is evidence for more specific polymer-polymer interactions (“hyperentanglements”). The concentration dependence and the time-scale of entanglement coupling have been monitored by both steady-shear and oscillatory measurements, and a generality of response has been demonstrated.

Linear and second-order pressure effects in velocity centrifugation of random coil polymers. Polystyrene in cyclohexane

Linear and second-order pressure effects in velocity centrifugation of random coil polymers. Polystyrene in cyclohexane

Quasielastic light scattering measurements of self-diffusion and mutual diffusion in gelatin solutions and gels

There has been considerable interest in comparing the mutual diffusion coefficients, measured by quasielastic llghtscattering, for a concentrated or semidilute uncross-linked polymer solution and for a cross-linked gel having identical or nearly identical chemical structure and the same polymer concentration. In several cases, the mutual diffusion coefficients have been found to be the same (JARRY and PATTERSON 1982) or closely similar (MUNCH, et al. 1977a, 1977b). In the study reported here, quasielastic light scattering measurements have been made on semidilute solutions of gelatin and the corresponding gels that are formed from these solutions at lower temperatures. Although gelatin is in a sense a poor choice of polymer because of its complex structure, uncertain gelation mechanism, and broad molecular weight distribution, it behaves above the gel temperature as a random coil polymer (VEIS 1964) and the viscoelasticity of its gels corresponds to that of a network of flexible strands (LAURENT, et al. 1980). In the present study, it has the unique advantage that viscoelastic measurements (LAURENT, et al. 1980) of the same gels have previously provided values of the translatory monomeric friction coefficient ~oas well as accurate values of the macroscopic shear modulus G, so the relation between scattering and mechanical measurements can be examined. From the scattering measurements on solutions above the gel temperature, the mutual diffusion coefficient D c is determined as well as a much smaller diffusion coefficient D 2 which can be identified as the self-diffusion coefficient of the polymer. For the gels, only D c is obtained, and its dependence on temperature and solvent viscosity (varied over a wide range by incorporation of glycerol up to 91% by weight) is examined. Over the range studied, both the friction coefficient ~o and the shear modulus G were previously observed to depend on both these variables (LAURENT, et al. 1980).

Influence of osmotic compression on calcium activation and tension in skinned muscle fibers of the rabbit.

Single skinned muscle fibers were osmotically compressed back to and below their in situ size by addition of a large, random-coil polymer (Deytran T500; MN = 180,000; MW = 461,000) to the bathing medium. Maximal Ca2+-activated tension in fibers swollen (zero Dextran, fiber width 21% above in situ) or near in situ size (5% Dextran, in g/100 ml final solution) was similar, but compression to 86% of in situ width with 10% Dextran decreased maximal force by 15% relative to polymer-free control. While the relative tension-pCa relation in 0 and 10% Dextran was similar, with a pCa of 6.37 required for 50% activation, that in 5% Dextran was more sensitive to Ca2+, with a pCa50 of 6.66. We feel these effects are most likely due to changes in interfilament spacing with compression and that alterations in Ca2+-sensitivity might be explained by changes in cross-bridge angle or in the concomitant attachment-detachment rate constants which would be expected to influence the troponin-Ca2+ binding equilibrium, as has been proposed by others.

Small-angle scattering of random coil polymer solutions

Small-angle scattering of random coil polymer solutions

Calculation of hydrodynamic parameters of random coil polymers from size exclusion chromatography and comparison with parameters by conventional methods

A new method of treating data from size exclusion chromatography, originally evaluated for native proteins, has been extended to random coil polymers using data from dextran and polyethylene glycol as specific examples. Columns are calibrated with globular proteins of known molecular weight. Multiplication by a constant transforms the abscissa to molecular radii. The constants in the equation r = gM Z are then evaluated directly from the size exclusion chromatographic data and compared with the corresponding constants obtained from viscometry, sedimentation velocity and light scattering, relating Stokes radius, root mean square end-to-end distance and radius of gyration to molecular weight.