Flexible Chain Molecules Research Articles

Mutual solubility of polymers and properties of their mixtures

AbstractHeats of mixing of polymers with each other have been measured, the behavior of the mixtures of solutions of various polymers has been studied, and the dependence of mechanical properties of polymer mixtures on the ratio of components has been investigated. It has been shown that mixing of polymers with each other is usually an endothermic process and, therefore, leads to formation of macroscopically homogenous, but actually microheterogenous, systems with an extremely high degree of dispersion. These microheterogenous polymer mixtures are formed because of the enormous viscosity of polymer mixtures, which prevents macroscopic separation into phases but does not hinder the considerable mobility of the segments of flexible chain molecules. It has been shown that the dependence of mechanical properties of microheterogenous polymer mixtures on the ratio of polymers in the mixture have sharp maxima or minima which cannot be found in the case of true polymers in polymer solutions. It has been found that the behavior of some polymer pairs is anomalous, in that exothermal mixing is supplemented by separation of the solution mixture into phases and by the appearance of maxima or minima in the dependences of the properties of polymer mixtures on the ratio of polymers in the mixture. This anomaly has been attributed to the effect of loose packing of the molecules of the polymers which show anomalous behavior. It has been shown that, in these systems, there necessarily exists a lower critical temperature of mixing whose value can be decreased by adding low‐molecular solvents to the loosely packed polymer. Attention has been drawn to the fact that, although mixing of amorphous polymers should be considered on a thermodynamic basis to be a mutual solution of two liquid phases, the large dimensions and the flexibility of polymer chain molecules require a critical revision of the possibility of formal application of the basis thermodynamic concepts and relations to a theoretical analysis of the behavior of polymer mixtures.

The Mutual Solubility of Polymers. I. Physicomechanical Properties of Stocks Prepared from a Mixture of Polymers

Abstract 1. The mixing of rubbers (or of any amorphous polymers) may be considered as a mutual solution of two liquid phases, conforming to thermodynamic laws. 2. The stocks studied, which were prepared from a base of a combination of different rubbers, fall into two groups as regards the nature of the relation between their mechanical properties and the proportions of the mixed rubbers. The opinion was expressed that the anomalies observed in the properties of combined stocks prepared from a mixture of SKS-30 and SKB are due to the micrononhomogeneous two-phase structure of such stocks. 3. It was shown that the properties of combined stocks are governed primarily by the behavior of the mixed rubbers themselves, and not by the ingredients incorporated into the stocks. 4. The compatibility of two polymers should be considered from two points of view. A macroscopic compatibility can almost always be achieved, provided that the polymer can be converted to the fluid state. However, compatibility in microregions, i.e., the mutual solubility of polymers, is determined by their thermodynamic properties and may not coincide with macrocompatibility. The reason for the discrepancy between macro- and microcompatibility is the chain structure of the polymer molecules, and the resulting large viscosity of polymers which have a high mobility of small segments of the flexible chain molecules.

Intermolecular Correlation in Light Scattering from Dilute Polymer Solutions

The effects of intermolecular correlation on light scattered from flexible chain molecules are considered. The random flight model is treated correctly to the double contact approximation. Two smoothed density models are carried to the same approximation and comparisons are made. In every case a decrease of ``apparent'' A2 with increasing angle of observation is predicted in qualitative agreement with experiment.

Random Flight Model in the Theory of the Second Virial Coefficient of Polymer Solutions

The theory of the second virial coefficient, A2(M2,T), for dilute polymer solutions is investigated from the point of view, first developed by Zimm, of the Ursell-Mayer-like development in terms which successively represent increasing numbers of contacts between molecular subunits of flexible chain molecules. The methods used by Fixman in treating excluded volume problems in the random flight model are here employed. Evaluation is carried out to the triple contact approximation. A formal analysis of all higher terms is presented and the contribution of one class of terms is evaluated exactly. The remaining terms appear to be inaccessible to numerical evaluation by ordinary methods so that a rigorous discussion of the asymptotic behavior of A2 is precluded. Semiquantitative arguments, however, indicate favorable agreement with experiment, provided intramolecular excluded volume effects are considered.

Physico-chemical studies of poly-d-glutamic acid from Bacillus anthracis grown in vitro

The behaviour of polyglutamic acid and of its alkali salts in aqueous electrolyte solutions of varying ionic strengths has been examined by light scattering and in the ultracentrifuge, and parallel diffusion and viscosity studies have been made. Both behave in solution as flexible chain molecules of effective volume large for their weight. The effective volume per mole is much greater for the ionized form than for the largely unionized form (free acid), and the effective volume of the alkali salts increases markedly with reduction in the ionic strength of the solvent as would be expected from their polyelectrolyte nature. Sedimentation studies indicate a substantial degree of ion-pair formation between the polyglutamate ion and the cation of the solvent electrolyte. Despite this, the alkali polyglutamates show a ‘secondary charge effect’ of considerable magnitude, much greater than that predicted from the measured electrophoretic mobility of the polyglutamate ion. In contrast to the free acid, both the sedimentation and diffusion coefficients are markedly concentration-dependent. These coefficients have been extrapolated to infinite dilution, the sedimentation coefficients on the assumption that their inverse varies linearly with concentration and the diffusion coefficients by the method of Mandelkern & Flory (1951 ), using a value of the second virial coefficient derived from light-scattering data. Combination of these extrapolated values leads to a molecular weight for the free acid of 172000 and for sodium polyglutamate of 200000 ± 5000 after allowance for the effects of selective solvation. Detailed analysis of the sedimentation data for sodium polyglutamate in salt solutions of varying density indicates that the molecule is selectively solvated with not more than its own weight of water, a more probable figure being approximately 60 %. Detailed light-scattering studies of sodium polyglutamate have been made at ionic strengths 0.2 and 1.1. The mean of a number of determinations gives a weight-average molecular weight of 238000 and a number-average of 88000, the latter figure being in good agreement with a value obtained by assay of free amino groups. Values of the root-mean-square end-to-end distance of coils having the number- and MATHS FORMULA-average molecular weights are also given.

Separation of hydrocarbon isomers by thermal diffusion

The separation of gaseous hydrocarbon isomers by thermal diffusion has been demonstrated, Experiments were made in a Clusius column and mixtures analyzed by a mass spectrometer. Binary mixtures ofn-pentane withneo-pentane,iso-pentane withneo-pentane,n-pentane withiso-pentane, andn-butane withiso-butane showed a marked degree of separation. In each case the former component concentrated in the cold zone. The phenomenon may be correlated with anomalies in the ratio between viscosity and thermal conductivity, which have previously been shown to occur for flexible chain molecules, and were attributed to the occurrence of ‘wrestling’ collisions between such molecules. Discussion in terms of an elementary theory of thermal diffusion leads to the conclusion that the more flexible molecules should concentrate in the cold zone. This is in complete accord with the expense: mental results.

Isothermal Viscosity-Molecular Weight Dependence for Long Polymer Chains

Evidence is given showing that the equation, logη=3.4 logZ+K, represents an empirical law of flow which holds generally for sufficiently long flexible chain molecules in bulk or in solution. Here η is the viscosity, Z is the number of atoms in the chain, and K is a constant which is dependent on the polymer type and on the temperature. All of the available data which cover wide molecular weight ranges for linear (and branched) molecules in bulk or in solution, including results on polyesters, polyamides, polystyrene, polyisobutylene, polydimethyl siloxane, and polymethyl methacrylate, support this conclusion. For chains having fewer than a critical number, Zc, of chain atoms (Zc being characteristic of the polymer species) the dependence of η on Z is less severe but more complex. These results are in semiquantitative agreement with the recent theory of F. Bueche. On the basis of this theory, values for the concentration of chain entanglements in various polymers are obtained from the observed values of Zc.

Dilute Solution Hydrodynamic Behavior of Flexible Chain Molecules: Polymethyl Methacrylate

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Sedimentation Behavior of Flexible Chain Molecules: Polyisobutylene

The sedimentation constants s0 at infinite dilution and the intrinsic viscosities [η] of five fractions of polyisobutylene have been determined in cyclohexane, a good solvent. Their osmotic molecular weights ranged from 3.1×104 to 1.4×106. Under the assumption that the effective hydrodynamic radii vary as the average linear dimensions of the molecule, f0/η0=P(〈r2〉)½ and [η]=Φ(〈r2〉)32/M, where f0 is the frictional coefficient, η0 is the viscosity of the solvent, 〈r2〉 is the mean-square end-to-end distance of the molecule, and P and Φ are constants. In confirmation, s0[η]⅓/M⅔ is constant throughout the molecular weight range investigated. Furthermore, Φ⅓P−1=2.5×106. The close agreement of this quantity with values for four other systems reported in the literature indicates that P, like Φ, is a universal constant for flexible chain molecules. It follows also that the observed proportionality of s0 (or of M/f0) to M0.42 instead of to M½ occurs because of intramolecular interactions which cause the molecule in solution to be expanded by a factor α which increases with molecular weight. The above theory accounts for both the sedimentation and intrinsic viscosity behavior of flexible chain molecules in a satisfactory manner. Neither the Kirkwood-Riseman nor the Debye-Bueche theories succeeds in doing so.

Thermoelastic properties of several biological systems.

Thermoelastic behaviour similar to that of rubber has been found in numerous biological systems : elastin fibres, heat-contracted collagenous and elastoidin fibres, resting muscle and fresh ‘silkworm’. In all these cases the elastic force must be attributed to the thermal motion of segments of partially stretched flexible chain molecules. We believe therefore that, generally, whenever high reversible extensibility is observed in living matter this latter contains a network of irregularly coiled or folded chain molecules. Such extensibility has been observed, for example, in animal membranes and in the elastic parts of cytoplasm. Several elastic systems contract on raising the temperature even if they are not subjected to a stress. These must contain two elastic systems which oppose each other : a system which contracts if the temperature is raised (such as does rubber under stress) and another one which is not affected in the same way by variation of temperature and maintains the stress of the first system. Such systems may be obtained by introducing cross-links in a stretched elastomer; in the case of collagenous fibres this can be achieved by treating with formaldehyde. Probably native elastin fibres contain a similar double system; they are not soluble in any of the solvents for proteins but become soluble under the action of elastase which seems to split up the cross-links. The ‘long-range’ elasticity of hair (and wool) keratin has given rise to a controversy ; according to Astbury, Speakman and Woods, the elastic force is due to the tendency of the long ‘ β ’ keratin modification to transform into the ‘ α ’ keratin modification which, according to these authors, has a lower energy. Other workers believe that the force is due to thermal motion. Now hair and wool are not highly extensible when dry ; the measured stress is due to short-range cohesive forces. It is only after these attracting forces between neighbouring groups are sufficiently weakened by swelling agents that keratin becomes extensible. Then, after relaxation, the ‘long-range’ force, due to thermal motion, eventually becomes predominant. The α-β transformation is thus not the cause of the ‘long-range’ retracting force, which has the same origin as that observed with other elastomers. The contracting force of tetanized muscle cannot be attributed to a ‘rubber-like’system. The stress-strain curve of tetanized muscle indicates that attracting forces are involved in muscular contraction.

The Frictional Coefficient for Flexible Chain Molecules in Dilute Solution

The frictional coefficient, f0, of a polymer molecule in dilute solution is assumed to vary directly as an average linear dimension of the chain. From this assumption equations are developed, as follows, which are analogous to those used successfully in the interpretation of intrinsic viscosity measurements; f0/η0 =KfM½α and Kf=P(〈r02〉/M)½ where α represents the factor by which the actual root-mean-square end-to-end distance exceeds the unperturbed distance (〈r02〉)½, M is the molecular weight, η0 the viscosity of the medium, and P should be a universal constant. Data in the literature on the dependence on molecular weight of sedimentation constants and diffusion coefficients, extrapolated to infinite dilution confirm the conclusions drawn from these equations.

Studies in polyelectrolytes. II. Gum arabate

Measurements of viscosity with varying concentration of solute, added sodium chloride, and the extent of neutralization of the solutions of gum arabate and arabic acid have been reported. A connected explanation for all the different observations has been formulated by the assumption of the existence of flexible chain molecules in solutions of gum arabate. From the same considerations the effect of pH variation with alkali on the relative viscosity of gum arabate solution has been attributed to the effect of sodium ion from alkali rather than the particular pH value.

Contribution to the discussion on the shape of the polystyrene molecule in dilute solutions by means of flow birefringence measurements

It is usually assumed that a chain molecule like polystyrene in dilute solutions is bent, and the question as to whether it is more or less rolled together has been put forward some time ago. Flow birefringence studies should be a fruitful approach to this question, but the theory of the Maxwell effect for chain molecules is very unsatisfactory. The author has recently developed the theory of the Maxwell effect for a solution of elastic impenetrable spheres. This model represents a limiting case like the model of a rigid sphere used successfully by Sadron and by Flory in the interpretation of viscosity measurements. The model could be a reasonable first approximation for flexible chain molecules, inasmuch as Debye and Bueche, as well as Kirkwood and Riseman find the impenetrable sphere as a limiting case in their more general theory of viscosity. The theory of the elastic sphere leads to some conclusions which are in agreement with experiments on the temperature dependence of the extinction angle at low gradients carried out with two samples of polystyrene. These results constitute a strong argument in favor of the model of a rather compact sphere for the polystyrene molecule. Also, the observed effect is completely different from the orientational effect characteristic of rigid molecules like tobacco mosaic virus; for polystyrene the origin of the phenomenon seems to be much more a deformation of an initially isotropic particle rather than an orientation of an elongated molecule. The results are on the other hand in disagreement with the theory of W. Kuhn and H. Kuhn based on a dumbbell model. In this short paper the author will summarize the results and put the emphasis on the possibilities of the flow-birefringence technique in the field of flexible chain molecules for the determination of the elasticity and the internal viscosity of these particles. Finally, a general method is suggested in order to check whether a chain molecule in solution is more or less rigid or flexible (extinction angle measurements at low gradients for several solvents with different viscosities).

Recent Trends in Polymer Chemistry

MACROMOLECULAR substances are equally interesting and important from the scientific and from the practical angle. Their behavior in solution and bulk can in most cases be explained by the existence of a network of entangled long flexible chain molecules, which attract each other by intermolecular forces and exhibit a certain tendency to form areas of higher geometrical order. The ultimate mechanical thermal, and electrical properties of such polymeric materials depend in a gather complicated manner on the various qualities of the individual macromolecules and it will be the purpose of this lecture to describe briefly our present knowledge of the connections between molecular structure and macroscopic properties of high polymers. The materials under consideration cover a wide range of mechanical behavior, some of them are soft and rubbery, others are soft and plastic, others again are very hard and rigid, and others finally are rough and flexible. From the practical point of view ...

On the Configuration of Chain Molecules. II

Abstract In order to express the apparent size of a flexible long chain molecule the radius of gyration σ around the centre of mass is an appropriate quantity, and its mean square 〈σ2〉 has been considered to be proportional to the number of elements of the chain n. We estimate the effect of the intramolecular interaction and find new equations &〈σ^2〉=const·n+const·n^1.5 &〈σ^2〉=const·n^1.5+const·n^2 Specific viscosity ηsp divided per weight concentration c must be &η_sp/c=const·n+const·n^1.5 \intertextor &η_sp/c=const·n^0.5+const·n In these equations the second term can never be neglected for large n. It amounts to one half of the first term even in the case of normal paraffine with only 100 carbon atoms. For large n the accurate formula η_sp/c=const.n^0.5+const.n^0.8 is obtained in the case of repulsive interaction, but in respect to the molecule of large molecular weight with attractive interaction the selfcoagulation into the very small size is concluded.

Les propriétés mécaniques du caoutchouc

A survey of recent work on the theories of the peculiar mechanical behaviour of substances with rubber-like properties is given. All the theories are based on the assumption that these substances (including rubber itself) are composed of very long, flexible chainmolecules. Any segment of a chain is linked to two neighbouring segments by bonds similar to those which are present in typical solids and to all other neighbours by linkages like the bonds prevailing between the particles of liquids. The chain molecules are intermingled so as to form a kind of a felt. This state of aggregation is intermediate between the solid and the liquid; it is called the rubber-like state (état gommoïdal). Elasticity, viscosity and plastic flow as well as the influence of crystallization, vulcanization and degradation are discussed in terms of this theory.

Application of the Methods of Molecular Distribution to Solutions of Large Molecules

The equations for the thermodynamic potentials of the solvent in solutions of ordinary organic molecules are extended to solutions of large molecules by methods using continuous molecular distribution functions. Particular attention is given to the coefficient, A2, of the second term in the expansion of the osmotic pressure in terms of the concentration, since this coefficient has a simple molecular meaning and is sufficient to describe the deviation of the system from ideality at low concentrations. A2 is calculated by direct integration for two rigid shapes, the sphere and the long thin rod. A general expression is then developed for A2 for flexible chain molecules in terms of the interactions of the segments of the chains. In favorable cases it is found possible to relate A2 for a chain molecule to the solution properties of its small molecule homologues by an equation very similar to those developed by Flory, Huggins, and Miller. In general, however, interactions that depend both on the local structure and also on the over-all shape of the chain molecules seriously modify such a relationship. The nature of these interactions, including the effects of branching and of limited flexibility, is discussed. It is also shown that higher coefficients in the expansion of the osmotic pressure in terms of concentration can be treated in a similar way. Comparison with experimental data confirms the general predictions of the theory both for proteins and chain polymers.