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The spacio—geotnetric characteristics of macromolecular chains are discussed from the point of view of the essential connections they provide between chemical constitution and properties. Quantities such as molecular weight, radius of gyration, degree of branching, etc., that characterize the molecule as a whole do not suffice for an understanding of the virtually endless variations in the properties that distinguish one polymer from another. For this purpose it is necessary to examine the chemical structures of the constituent units, taking into account the geometric parameters pertaining to chemical bonds, the conformations accessible to the chain skeleton and the resulting spatial configurations. The physical principles underlying the statistical mechanical treatment of conformations of long chain molecules and of their configuration—dependent properties are summarized. Correlations between bonds of the chain and the range of such correlations provide insights into the spatial characteristics of polymer chains. Persistences expressing the configurational averages of vectors spanning sequences of chain units are particularly useful in this connection. Experimental methods that provide quantitative information on conformation and the correlations between units of the chain are briefly discussed.

The effects of restrictions on the fluctuations of network junctions imposed by neighboring chains are treated by resort to a model in which these restrictions are represented by domains of constraint. Whereas in a phantom network devoid of such constraints the displacements of junctions from their mean positions are invariant with strain, involvements with neighbors in a real network render them dependent on the strain. The observed stress consequently is increased above predictions for the equivalent phantom network. On the plausible assumption that the dimensions of the domains are transformed linearly (affinely) by the macroscopic strain, the constraints become less restrictive in the direction of a principal extension λt with increase in λt. Hence, the relative enhancement of the stress diminishes with the strain. The characteristic departures of the observed tension (ƒ)-extension (α) curve for elongation from the expression ƒ α kT(α−α−2) of previous molecular theories are qualitatively reproduced by the present theory, which also accounts for the approximate constancy of ƒ/(α−α−2) observed in compression and the decrease of this ratio with dilution.

Expressions are derived for the osmotic pressure and turbidity of a dilute solution of two chemically dissimilar polymer species in a solvent. The relations obtained are contrasted with those derived through use of the free energy of mixing as given by the quasi‐crystalline lattice model. Use of equations based on the lattice model to evaluate polymer‐polymer interaction parameters from dilute solution data is shown to be valid only in special instances.

A useful approximation has been found for the excluded volume integral for the interaction of a pair of polymer molecules, represented by Gaussian distributions of chain segments about their respective centers of gravity. By means of this approximation, the theoretical expression for the second virial coefficient in the expansion of the osmotic pressure is represented over the entire range of polymer‐solvent interaction by A2=const ([η]/M) ln[1+(π12/4)X1+(π12332/32)X2].X1 and X2 are related to the thermodynamic interaction parameters χ1 and χ2, respectively, in the semiempirical expression for the solvent chemical potential μ1—μ10=RT[ln(1—v2)+(1–1/x)v2+χ1v22+ χ2v23+···] where v2 is the volume fraction of polymer and x the ratio of molar volumes of polymer and solvent. Inclusion of the higher term χ2v23 (and X2) constitutes a refinement over the treatment previously published. It is shown that the influence of X2 may be appreciable for low molecular weights and in poor solvents; its effect vanishes as the ...

The excess volumes VE of mixtures of polystyrene with methyl ethyl ketone determined at 25°C are negative. At a segment fraction ϕ2= 0.5 of polymer, VE is ca. 0.9 % of the total volume. Osmotic pressures have been measured from ϕ2= 0.10 to 0.35 at 10° and at 50°C. The temperature coefficient of the reduced residual chemical potential χ indicates a very small positive heat of mixing in accord with vapour pressure measurements of Bawn, Freeman and Kamaliddin at higher concentrations. The recent statistical thermodynamic theory of solutions which relates their properties to characteristics of the pure liquids manifested in the equation-of-state parameters succeeds in accounting for the principal features of this system. This theory correctly predicts the sign of the excess volume, although it underestimates its magnitude. It also accounts for the observed increase of χ with concentration, and for the small negative entropy of dilution at low concentrations, with change of sign at ca.ϕ2= 0.05. Thermal expansivities and thermal pressure coefficients for methyl ethyl ketone have been measured from 20° to 60°C with an accuracy of ±1 % or better.

Stress—strain isotherms are presented for poly‐(dimethylsiloxane) networks of different degrees of cross linking, swollen to various extents by a diluent. Results are interpreted in terms of the equation f*v213V*/(α−α−2)=2C1+2C2α−1, where f* is the tension per unit initial area (unswollen) exhibited by a network when swollen to a polymer volume fraction v2 and elongated to the relative length α, 2C1 is a parameter of the network structure established by the molecular theory of rubber elasticity, and 2C2 is an additional parameter found to give a better representation of experimental data. Values of C2 obtained for networks are found to decrease as the degree of cross linking is decreased, and the degree of swelling is increased.

Thermoelastic measurements conducted at constant pressure on systems of fixed composition must be corrected to constant volume in order to achieve the desired resolution of the stress into its energy and entropy components. In the case of simple elongation deduction of the energy component f9 =(∂E/∂L)T,V = [∂(f/T)/∂(1/T)]L,Vof the tension f from measurements at constant pressure requires the equation of state p(T, V, L), or equivalent information. If the system is a polymer network swollen with a diluent or a diluent mixture, and equilibrium is maintained with a surrounding diluent phase, additional complications may arise from changes in composition with deformation and/or temperature. If, however, the diluent mixture is so chosen as to render the equilibrium volume of swelling independent of temperature, then, as we have pointed out previously, fe may be equated to the coefficient = [∂(f/T)/∂(1/T)]L,p,eq, which may be determined directly from measurements on the system maintained in equilibrium with excess diluent. The basis for this simplification is set forth in detail. The conversion of measurements conducted at constant pressure to constant volume is obviated by this procedure, and a simple means is provided for evaluating the internal energy changes accompanying distortion of a polymer network and the concurrent orientation of the chains of which it is composed. Allegations that the indicated procedure is invalidated by disregard of changes of composition of the network phase with temperature and deformation are unfounded. Inconsistencies in recent publications on the analysis of thermoelastic data for networks in swelling equilibrium are pointed out.

The length of the span of the terephthaloyl residue in poly(ethylene terephthalate) guarantees independence of the conformations of successive repeating units of the chain. Interactions within units of the chain are amenable to interpretation by comparisons with related polymers; cis and trans conformations of the terephthaloyl residue are given equal weighting. The mean-square dimension ratio (〈r2〉0/M)∞ estimated on this basis is in substantial accord with the value deduced from experiments.

A general theory is presented on the effect of elongation of a polymer chain on the apportionment of its bonds and bond sequences among various rotational isomeric states. The perturbation of the population of a state η is found to be proportional to 32[(r2 / 〈r2〉0) − 1][(〈rη;i2〉0 / 〈r2〉0) − 1], where r is the length of the chain vector, 〈r2〉0 is the mean square of r for the unperturbed chain, and 〈rη;i2〉0 is the same quantity subject to the condition that the bond i or bond sequence i is in the conformational state specified by η. The theory is limited to the range of moderate deformations; it is inapplicable for lengths r approaching full extension of the chain. Numerical calculations are presented for polymethylene chains and for syndiotactic vinyl polymers. The calculated effects are very small; unit increase in r2 / 〈r2〉0 generally alters the conformation population of a given state by no more than about one bond (or sequence) per chain. The length of the given conformation and its susceptibility to ...

Geometrical and spatial characteristics of macromolecular chains are determined by bond lengths, bond angles and hindrances to rotations about skeletal bonds as expressed by the conformational energies associated therewith. The presence of cyclic structures or of double bonds within the backbone may alter the configurational behaviour markedly. The structures of familiar polymeric substances present wide variations in these respects. Mathematical methods now available enable one to evaluate average properties of randomly coiled polymer chains of almost any description, full account being taken of all configurations of the molecule. These methods are exact, being subject only to the scheme adopted for describing bond conformations. The rotational isomeric scheme is generally applicable for this purpose, although more refined models may be employed for complicated chains such as the polypeptides and poiynucleotides. The nature of the methods is described and configurational characteristics of representative chains are reviewed. Artificial models such as the freely jointed chain and the wormlike chain are incapable of representing the diversity of chemical structures that are of interest. These models tend to obscure rather than clarify the connections between properties and structure of polymeric chain molecules, which can now be treated in realistic fashion by newer methods.

According to the molecular theory of rubber elasticity, the stress τ is related to the relative length α in simple extension according to τ=kT(ν/V) 2(α−1/α2), where (ν/V) 2 is a parameter of the network structure. Improved agreement with experiment has been claimed through use of the relation τ=(2C1+2C2/α) (α−1/α2) which contains the additional parameter C2. In order to explore factors affecting this theoretically inexplicable term, stress‐elongation measurements were performed on networks prepared from natural rubber, Butyl rubber, poly‐(dimethylsiloxane), poly‐(ethyl acrylate), and poly‐(methyl methacrylate) under a wide range of experimental conditions. Results may be summarized as follows: (1) the C2 term offers improved agreement over the extension phase of an elongation cycle, but not for the subsequent retraction phase; (2) apparent values of C2 (determined on extension) vary widely from one polymer to another, increasing with hysteresis and with proximity to the glass transition temperature; (3) they are insensitive to the degree of cross linking; (4) C2 is markedly reduced by permanently swelling the network with a diluent, or by swelling and deswelling the sample at each tension; (5) incorporation of diluent prior to establishing a network by cross linking with gamma radiation likewise lowers C2, the value characteristic of the unswollen polymer being restored upon removal of the diluent. The results demonstrate that the controversial C2 term arises from the difficulty of attaining elastic equilibrium; under ideal experimental conditions the value of this parameter becomes negligible. An alleged limitation of the theory of rubber elasticity is thus refuted.

The absolute density, thermal expansion coefficient α, and thermal pressure coefficient γ have been determined for atactic polystyrene in the non-glassy liquid (or amorphous) state. Dilatometric measurements on the pure polymer furnished α over the range 100° to 230°C. Thermal pressure coefficients were determined by extrapolation from measurements on concentrated solutions of the polymer in benzene, from 24° to 100°C. No evidence was found for a second order transition above 100°C. A small change in dα/dT was observed near 170°C. This and other observations suggest a minor departure from equilibrium below this temperature.

Stress strain isotherms are presented for poly (dimethylsiloxane) networks of different degrees of crosslinking, swollen to various extents by a diluent. Results are interpreted in terms of the equation f*v21/3V/(α−α−2)=2C1+2C2α−1, where ƒ* is the tension per unit initial area (unswollen) exhibited by a network when swollen to a polymer volume fraction v2 and elongated to the relative length α, 2C1 is a parameter of the network structure established by the molecular theory of rubber elasticity, and 2C2 is an additional parameter found to give a better representation of experimental data. Values of C2 obtained for networks are found to decrease as the degree of crosslinking is decreased, and the degree of swelling is increased.

According to the molecular theory of rubber elasticity, the stress τ is related to the relative length a in simple extension according to τ=kT(ν/V)〈α〉2(α−1/α2), where (ν/V)〈α〉2 is a parameter of the network structure. Improved agreement with experiment has been claimed through use of the relation τ=(2C1+2C2/α)(α−1/α2) which contains the additional parameter C2. In order to explore factors affecting this theoretically inexplicable term, stress-elongation measurements were performed on networks prepared from natural rubber, Butyl rubber, poly-(dimethylsiloxane), poly-(ethyl acrylate), and poly(methyl methacrylate) under a wide range of experimental conditions. Results may be summarized as follows: (1) the C2 term offers improved agreement over the extension phase of an elongation cycle, but not for the subsequent retraction phase; (2) apparent values of C2 (determined on extension) vary widely from one polymer to another, increasing with hysteresis and with proximity to the glass transition temperature; (3) they are insensitive to the degree of crosslinking; (4) C2 is markedly reduced by permanently swelling the network with a diluent, or by swelling and deswelling the sample at each tension ; (5) incorporation of diluent prior to establishing a network by crosslinking with gamma radiation likewise lowers C2, the value characteristic of the unswollen polymer being restored upon removal of the diluent. The results demonstrate that the controversial C2 term arises from the difficulty of attaining elastic equilibrium; under ideal experimental conditions the value of this parameter becomes negligible. An alleged limitation of the theory of rubber elasticity is thus refuted.

The thermal expansivity α=V−1(∂V/∂T)p and thermal pressure coefficient γ=(∂p/∂T)v for poly(dimethylsiloxane) (PDMS), mol wt ≈ 105, have been determined accurately over the temperature ranges 20–207 and 24–161°, respectively. Characteristic parameters ν*, T*, and p* calculated from these results are compared with those for other polymers and for low molecular weight liquids. For PDMS, α is much larger and γ much smaller than for any other polymer. The characteristic pressure p* appears to be a more reliable index of the intermolecular energy than the cohesive energy density for this purpose. It is approximately the same for a polymer as for corresponding low molecular weight liquids. For PDMS and HMDS (hexamethyldisiloxane) p* assumes exceptionally low values of 341 and 358 J cm−3, respectively, which are duplicated only by the fluorocarbons (p* ≈ 360 J cm−3).

Restrictions on freedom of rotation about the bonds of a polymer chain usually impose drastic limitations on the conformational states of polymer chains, and hence are of foremost importance in affecting the tendency of the polymer to crystallize. The severity of these restrictions notwithstanding, the random coil form almost always prevails when the molecules are dispersed in dilute solution. The conformation of minimum energy, represented by one of several helical forms, or by the planar trans conformation, ordinarily is manifested only in the crystalline state. Important exceptions are provided by polypeptides and related polymers of biological interest; owing to strong co-operative interactions between neighboring units, the characteristic helical form retains stability in dilute solutions under suitable conditions. Various first-order transitions which are observed to occur in polymers are discussed. These include (1) the widely observed crystallization and melting of polymers, the crystalline phase comprising close packed molecular chains in their preferred rodlike (helical) conformations; (2) dissolution (and re-aggregation) of the crystalline polymer to yield a dispersion of individual molecules without alteration of conformation, as exemplified by preparation of solutions of native collagen, and reversal of the process with reconstitution of fibrils; and (3) the now familiar helix–coil transition featured by proteins and synthetic polypeptides dispersed in dilute solution. The helix-coil transition may be regarded as the most primitive manifestation of polymer melting and crystallization. In order to separate influences of molecular geometry, intermolecular interactions, and solution concentration on the one hand from intrinsic intramolecular factors on the other, it is advantageous to regard (1) as the sum of (2) and (3). A further phase transition, previously predicted by theory and recently observed by Robinson, Ward, and Beevers in solutions of poly-γ-benzyl-L-glutamate in various organic solvents, is manifested by separation of an anisotropic phase from moderately dilute solutions, of highly anisometric, rodlike particles. This tactoidal phase is only slightly more concentrated than the parent isotropic phase. The rates of the helix ⇄ coil transformations are advantageously treated as stepwise processes through use of the mathematical theory of gambler's ruin.

Consider a homopolymer consisting of rigid and flexible sequences in alternating succession. The prototype isThe degree of polymerization DP is very large. The oxyethylene units may occur in various disordered conformations or in the ordered one, ttt, with a statistical weight s* compared with unity for the disordered forms, collectively. Let γζ be the number of rigid sequences containing ζ rigid units, i.e., consisting of ζ rigid members joined by ζ-1 oxyethylene units in extended (ordered, ttt) conformations, the oxyethylene units flanking this sequence being otherwise conformed.

The molecular features responsible for liquid crystallinity are: (i) asymmetry of molecular shape and (ii) anisotropy of intermolecular forces. The former feature is dominant, especially among polymers.1,2 Feature (ii) is most prominent in liquid crystalline compounds of low molecular weight; it is doubtless important also in many polymers containing groups, such as p-phenylene, whose polarizabilities are highly anisotropic. The latter feature, although of lesser importance than (i) in promoting liquid crystallinity, is usually responsible for thermotropic behaviour.

ABSTRRACTTheory predicts that the nematic state of a homopolymer comprising rigid and flexible sequences in alternating succession depends critically on the tendency of the flexible units to reconform to ordered extended conformations. When the relative statistical weight s* of such extended conformations is very small (very flexible), the chains undergo only a minor conformational rearrangement in the nematic state. Moreover, the clearing temperature and the orientational order of these nematic polymers are not much different from those of the monomeric liquid crystals. Hlowever, as the value of s* becomes larger than a certain critical value, an ordered (nematic) state exhibiting perfect orientational order and completely rodlike conformations becomes more stable than the state of only partial order. Hlence, an extensive conformational rearrangement is predicted to occur in nematic melts of the polymers when the flexible sequences are niot very flexible. These predictions are in good qualitative agreement with the conclusions from the thermodynamic and NMR measurements on two thermotropic polymers comprising identical rigid groups joined by flexible sequences of substantially different flexibility.

Formulation de l'energie libre de dilution de reseaux. Cas de reseaux non charges et ioniques ou une petite proportion de groupes ionisables modifie le comportement thermodynamique

The optical anisotropies γ2 and molar Kerr constants mK of C6H5X, p-CH3—C6H4—X and p-(CH3)2CH—C6H4—X where X = Cl or Br, and of atactic poly(p-chlorostyrene) have been determined from depolarized Rayleigh scattering and electric birefringence measurements in CCl4 solutions at 25°C using λ= 633 nm radiation; γ2 for poly(p-bromostyrene) was determined in a mixture of CCl4 and CBr4. The anisotropic part of the polarizability tensors for C6H5Cl and C6H5Br are well defined by γ2 and the molar Cotton–Mouton constant mC, values of which are available from the work of LeFevre and co-workers for these two compounds. Owing to the orientation of the dipole moment along one of the principal axes of , this tensor cannot be evaluated unambiguously from mK and γ2 for the other compounds. The anisotropy attributable to the arylene group about the axis joining the substituents appears to be little affected by substitution, however. Asymmetry of the arylene group perpendicular thereto depends appreciably on substitution; bond and group polarizabilities are not additive. The anisotropies of the polymers are formulated as the sums of tensors for the corresponding p-halogenocumenes. Averages 〈γ2〉 and 〈mK〉 over all conformations of the polymer chains are calculated as functions of the fraction wm of meso dyads. Values of 〈γ2〉 decrease about three-fold from syndiotactic (wm= 0) to isotactic (wm= 1). 〈mK〉 is extraordinarily sensitive to stereochemical composition; it decreases from a large positive value for wm= 0 to a large negative value for wm= 1. These results are interpreted in terms of structure and preferred conformations. Experimental measurements on atactic polymers support the calculations.

This investigation represents an attempt to understand why noncrystalline rubber‐like polymers suddenly lose their flexibility and become brittle when cooled to a particular temperature, and conversely why an amorphous plastic such as polystyrene when heated to a particular temperature suddenly becomes either flexible and rubbery or fluid.

When di(isobutylamino)phenylboron is pyrolysed, isobutylamine is eliminated and the trimer, B-triphenyl-N-tri-isobutylborazine, is produced. Contrary to claims in the literature, the pyrolysis does not provide a route to linear boron–nitrogen polymers.

The mean-squared optical anisotropies 〈γ2〉 of four oligomers of polyoxyethylene glycol dimethyl ether have been determined from measurements of depolarized Rayleigh scattering by carbon tetrachloride solutions at 25°C. They have been interpreted using the valence optical scheme and rotational isomeric state theory. The energies of the gauche states relative to trans were taken to be 900 cal mol–1 and –250 cal mol–1 for rotations about C—O and C—C bonds respectively. Gauche states of opposite signs for C—O—C bond pairs were excluded; those for C—C—O bond pairs were assigned an energy of 800 cal mol–1. Bond optical anisotropies were assigned the values ΔαCC= 0.95 A3, ΔαCH= 0.21 A3, and ΔαCO= 0.58 A3. Calculations of 〈γ2〉 carried out with these parameters successfully reproduce the observed values of 〈γ2〉. The foregoing rotational state energies are in close agreement with those deduced previously from the characteristic ratio 〈r2〉0/nl2 for the polymer, from the dipole moments 〈µ2〉 of oligomers and polymer, and from the temperature coefficients of these quantities.