Phase equilibrium diagrams are the basis of materials science. Phase diagrams of two-component systems "polymer - solvent" Phase diagrams of two-component systems "polymer - solvent"
Entropy of mixing for the polymer-solvent system
Consider a mixture of two liquids, one of which is a polymer. In this case, the above model can be used, but the entropy of mixing for the solvent-polymer system will be different. Obviously, the change in entropy will be smaller, since the monomer units of the polymer are not able to fully utilize the increase in volume upon mixing. This is prevented by the "cohesion" of the monomers in the polymer. And the mixing energy has the same form as for a mixture of two low molecular weight liquids.
Consider a solution consisting of H solvent molecules and N2 polymer molecules with a degree of polymerization r; the total number of solvent molecules and monomer units is equal to H = N + Nir. The entropy of mixing of such a system is expressed by the equation
Then the expression for the entropy of mixing can be written in the usual form:
The total number of moles is defined as the number of moles of solvent and polymer segments in the system . The entropy of mixing per one mole of a substance is given by
Rice. four.
The mixing energy has the same form as for a mixture of low molecular weight liquids); let's write it in the form
It is interesting to analyze the difference in entropy change when mixing two simple liquids and mixing a simple liquid and a polymer. Let's define this difference AAS:
Thus, the value AAS increases with the length of the polymer molecule, and, as a consequence, it can be expected that the phase separation of the polymer–solvent mixture should occur at an earlier stage, i.e., at a lower temperature than the phase separation of mixtures of two low molecular weight liquids.
Phase equilibrium in the Flory-Huggins theory
From the equations, and the free energy of mixing per mole can be expressed by an equation where the first term is the change in energy, and the second is the change in entropy during mixing. The derivative of this expression with respect to component 1 corresponds to the chemical potential of the solvent in the binary solution:
Rice. 5.
A nonmonotonic change in the chemical potential indicates a phase separation of the system. It is interesting to find out at what value of q this occurs. After some algebraic transformations, we find that the critical point is determined by two expressions:
It makes sense to compare the values of the critical parameters for polymer solutions with the corresponding parameters for regular solutions xc = 2ifc = 0.5. It can be seen that polymer solutions become incompatible more easily and separate into phases).
I-Temperature
The concept of n-temperature and the notion of good and bad solvents is widespread in polymer science. To introduce these concepts, we return to the equation. The excess chemical potential for small volume fractions of a solute can be expanded into a series:
where theta temperature is defined as
The equation shows that when the physical temperature is equal to the theta temperature, the system behaves like an ideal solution, i.e., Dm = 0. If F > and, the solvent is a good solvent for the polymer, and if F< and - a bad solvent. In addition, one can interpret the 0-temperature in another way, using the critical temperature at which the first phase separation of the polymer solution occurs:
Rice. 6.
Thus, from the equation, the u-temperature can be determined as the critical temperature for an infinitely long polymer.
RHEOLOGY- the science of deformations and fluidity of continuous media that exhibit elastic, plastic and viscous properties in various combinations. Elastic deformations occur in the body when a load is applied and disappear if the load is removed; plastic deformations appear when the stresses caused by the load exceed a known value - the yield strength; they persist after unloading; viscous flow is distinguished by the fact that it occurs at any arbitrarily small stresses, with increasing stresses the flow velocity increases, and while maintaining stresses, the viscous flow continues indefinitely. Another property that can be possessed by media studied by rheology is high elasticity, which is typical, for example, for rubber, when a rubber band allows tenfold stretching, and after removing the load, almost instantly restores its original state.
A typical rheological process is a relatively slow flow of a substance in which elastic, plastic or highly elastic properties are found. Rheological phenomena are manifested in many natural processes and in a large number of technological ones. The substances involved in such processes are very numerous: these are the rocks that make up the earth's crust, magma, volcanic lava, these are oil and clay solutions that play a crucial role in oil production; wet clay, cement paste, concrete and asphalt concrete (a mixture of asphalt and sand that covers the sidewalk), these are oil paints - a mixture of oil and pigment particles; these are solutions and melts of polymers in the process of manufacturing threads, films, pipes by extrusion; finally, these are bread dough and pasty masses, from which sweets, sausages, creams, ointments, toothpastes are made, this is solid fuel for rockets; these are, finally, protein bodies, for example, muscle tissues.
THERMODYNAMICS OF SPONTANEOUS DISSOLUTION OF POLYMERS
The dissolution of polymers is similar to the unlimited mixing of two liquids, which obeys the second law of thermodynamics. The second law of thermodynamics is a general pattern that allows you to find the direction and establish the possibility or impossibility of thermodynamic processes. According to the second law, heat cannot spontaneously transfer from a less warm body to a warmer one.
The processes in which thermal phenomena are involved spontaneously go in only one direction and stop after the state of thermodynamic equilibrium is reached - a more "preferred" state. Entropy is a state function that characterizes the measure of this “preference”. In an isolated system, only such processes are possible in which the entropy increases or remains unchanged.
The thermodynamic condition for spontaneous dissolution - the change in the free energy of the system during spontaneous dissolution must be negative:
ΔG = ΔH-TΔS<0,
where ΔН is the change in enthalpy, or the enthalpy of mixing; ΔS is the change in entropy, or the entropy of mixing; T is the absolute temperature. There are three possible cases here:
1) ΔG<0- при растворении происходит поглощение тепла (эндотермическое растворение);
2) ΔG>0 - during dissolution, heat is released (exothermic dissolution);
3) ΔG=0 - no heat is absorbed or released (athermic dissolution).
Compliance with the thermodynamic dissolution condition ΔG<0 возможно при следующих условиях:
1) under the condition Δ H< 0, которое соблюдается, если при растворении выделяется теплота, так как изменение энтальпии (или внутренней энергии) равно интегральной теплоте растворения с обратным знаком. Такое условие часто соблюдается на практике, например, при растворении полярных полимеров в полярных растворителях. Положительный тепловой эффект при растворении объясняется тем, что теплота сольватации макромолекул больше теплоты собственно растворения, а как известно, общий тепловой эффект растворения равен алгебраической сумме теплот сольватации и собственно растворения;2) under the condition Δ S> 0, which is always carried out in practice during dissolution, since the entropy of mixing is always positive. The entropy of mixing HMS with a solvent, calculated per weight fraction of a substance, lies between the values of the entropy of dissolution of low molecular weight substances and typical colloidal systems.
Often, when the IUD is dissolved, the dissolution process proceeds exclusively due to a change in entropy (in the direction of increase), i.e., athermally. The effect of temperature should also be taken into account. If the polymer does not dissolve at a certain temperature (ΔН-TΔS>0), then with increasing temperature the absolute value of TΔS may become greater than the absolute value of ΔН, and then the inequality sign will change to the opposite. This temperature is called the critical mixing temperature.
The theory of polymer solutions, developed using thermodynamics and based on the analogy between the dissolution of polymers and the unrestricted mixing of two liquids, has a number of shortcomings due to the many assumptions and corrections in determining both the entropy of mixing ΔS and the heat of mixing ΔН of a polymer with a solvent.
Phase equilibrium in the polymer-solvent system
The stability of the system (phase equilibrium), as a rule, is determined by the degree of thermodynamic affinity of the components, depends on their chemical composition and structure, external conditions, in particular, on temperature. The main law of equilibrium of a multiphase multicomponent system is the Gibbs phase rule, which establishes the relationship between the number of phases F, the number of components in the system K and the number of its degrees of freedom C:
The number of degrees of freedom shows how many thermodynamic variables that determine the state of the system (pressure, temperature, etc.) can be changed arbitrarily without causing a change in the number of phases in the system, that is, without disturbing its equilibrium.
In systems in which the components are only in liquid and solid states, the change in pressure has little effect on the properties, so the pressure can be considered constant, and the equation of the phase rule takes the form
According to this equation, a two-component single-phase system has two degrees of freedom (the state of the system is determined by the temperature and concentration of one of the components). In the presence of two phases (Ф = 2), the two-component system has one degree of freedom. This means that a change in temperature causes a change in the concentration of both phases. At some temperature, these phases can merge to form a single-phase homogeneous solution. Conversely, a single-phase homogeneous solution at a certain temperature can delaminate or separate into two phases. The temperature at which separation occurs is called the phase separation or phase separation temperature (TfP). A solution of each concentration has its own GphR, the dependence of which on the composition of the solution is expressed by a mutual mixing curve, or a boundary curve that separates the region of single-phase solutions from two-phase ones.
Depending on the composition of single-phase two-component liquid solutions during their cooling, two cases of separation into constituent components are possible: liquid and crystalline. With liquid separation, one liquid phase is separated into two liquid phases, with crystalline separation, a component in the form of a crystalline phase separates from the solution.
The stability of the system (phase equilibrium), as a rule, is determined by the degree of thermodynamic affinity of the components, depends on their chemical composition and structure, external conditions, in particular, on temperature. The main law of equilibrium of a multiphase multicomponent system is the Gibbs phase rule, which establishes the relationship between the number of phases F, the number of components in the system K and the number of its degrees of freedom C:
The number of degrees of freedom shows how many thermodynamic variables that determine the state of the system (pressure, temperature, etc.) can be changed arbitrarily without causing a change in the number of phases in the system, that is, without disturbing its equilibrium.
In systems in which the components are only in liquid and solid states, the change in pressure has little effect on the properties, so the pressure can be considered constant, and the equation of the phase rule takes the form
According to this equation, a two-component single-phase system has two degrees of freedom (the state of the system is determined by the temperature and concentration of one of the components). In the presence of two phases (Ф = 2), the two-component system has one degree of freedom. This means that a change in temperature causes a change in the concentration of both phases. At some temperature, these phases can merge to form a single-phase homogeneous solution. Conversely, a single-phase homogeneous solution at a certain temperature can delaminate or separate into two phases. The temperature at which separation occurs is called the phase separation or phase separation temperature (TfP). A solution of each concentration has its own GphR, the dependence of which on the composition of the solution is expressed by a mutual mixing curve, or a boundary curve that separates the region of single-phase solutions from two-phase ones. Depending on the composition of single-phase two-component liquid solutions during their cooling, two cases of separation into constituent components are possible: liquid and crystalline. With liquid separation, one liquid phase is separated into two liquid phases, with crystalline separation, a component in the form of a crystalline phase separates from the solution.
21. Viscosity of polymers. Viscosity anomalies.
IUD solutions only at very high dilutions (~0.01%) obey the laws of Newton and Poiseuille. A characteristic feature of HMS solutions is their high viscosity compared to a pure solvent, even at low concentrations.
Viscosity(internal friction) is the property of liquids to resist the action of external forces that cause them to flow. In addition, HMS solutions are not Newtonian fluids, since their viscosity (η) depends on the shear stress (R)- the ratio of the force tangentially applied to the sample to the unit surface (Fig. 14.7).
The reasons for the viscosity anomaly lie in the presence of structural viscosity in such systems. Structural viscosity- this is the additional viscosity due to the additional resistance to flow from the side of the internal supramolecular spatial structures - networks, threads, large drops of emulsions. The viscosity of such systems does not remain constant with increasing shear stress, but drops sharply until it reaches a constant value, but at a lower level due to the destruction of the structure (Fig. 14.8).
Rice. 14.7. Dependence of the viscosity of solutions of low-molecular substances of Newtonian liquids (1) and HMS solutions (2) on shear stress
This property is especially pronounced in polymers with long linear molecules, such as rubber. Solutions of polymers with the same molecular weight, but with a spherical shape of the molecules, have a lower viscosity. Hence it follows that the viscosity of polymer solutions increases in proportion to the asymmetry of their molecules. With the same chemical structure, the viscosity increases with increasing molecular weight. It also depends on the polymer concentration and intermolecular forces of interaction.
Rice. 14.8. Change in the Structure of HMS Solutions with Increasing Shear Stress
The region of constancy of viscosity of anomalously viscous liquids is called pseudoplastic area. A further increase in shear stress causes an increase in the viscosity coefficient, which is associated with turbulence.
Experimental data show that colloidal anomalously viscous systems can flow even at very low pressures, while the viscosity remains constant, but very high. Such a flow is called creep.
An increase in pressure sharply reduces the viscosity of creeping systems until the second region of viscosity constancy, the pseudoplastic one, sets in.
Viscosity anomalies are caused by a number of reasons.
1. Structure formation - the process of aggregation of particles of colloidal solutions, suspensions, IUD solutions and the formation of spatial easily destructible structures.
2. Change in the orientation of elongated particles and macromolecules in the flow with an increase in the velocity gradient.
3. Deformation of coils of polymer macromolecules or drops of emulsions in a flow.
With an increase in temperature, the viscosity of structured systems sharply decreases due to the destruction of the structure. As the temperature decreases, the proportion of structural viscosity increases significantly.
HIGH MOLECULAR COMPOUNDS, 2010, Volume 52, No. 11, p. 2033-2037
UDC 541.64:536.6
PHASE EQUILIBRIUM IN POLYMER-SOLVENTER SYSTEMS:
DEVELOPMENT IN THE FIELD OF FIBER
M. M. Iovleva and S. I. Banduryan
Limited Liability Company "LIRSOT" 141009 Mytishchi, Moscow Region, st. Kolontsova, 5
A brief review of the development of the scientific direction on phase equilibria of polymer-solvent systems is given. The features of phase diagrams intended for obtaining fibers with high strength, deformation and thermal properties are considered. Attention is drawn to the fundamental role of S.P. Papkov in the creation and development of scientific concepts of phase equilibria in fiber-forming polymers with the participation of solvents.
The history of the systematic study of phase equilibria in systems containing fiber-forming polymers dates back more than seven decades. In 1936 V.A. Kargin and S.P. Papkov began to outline the foundation of such a teaching. The following year, the results of observations of the unusual behavior of cellulose diacetate solutions as a function of their concentration and temperature were published. The behavior of these polymer solutions, in essence, was completely similar to the behavior of such a low-molecular substance as phenol, which forms in water in different temperature-concentration regions either a true single-phase solution or two liquid phases in equilibrium. These studies of solutions of diacetate and other cellulose ethers, in particular nitrates, were started at the Scientific Research Institute of Artificial Fiber (Mytishchi). In 1937, a well-known article by S.P. Papkova, V.A. Kargina, Z.A. Rogovin, in which the polymer-solvent phase diagram was constructed for the first time and conclusions were drawn about the possibility of the formation of not only colloidal, but also molecular-dispersed solutions by polymers.
To these results, which have become textbooks, it should be added that in the same years, studies were also begun on ternary systems polymer-solvent-precipitator, described, as a rule, using the plane of a triangle. The work of that period was associated only with amorphous equilibria. But soon they initiated research and solutions of a well-crystallized polymer - polyethylene. These are the works of Richards, in which the coexistence of bino-
Email: [email protected](Iovleva Margarita Mikhailovna).
distances and liquidus curves, i.e., amorphous and crystalline equilibria.
Thus, in the 30s and 40s of the 20th century, the doctrine of phase equilibria in systems of amorphous and crystallizing, and mainly fiber-forming, polymers emerged.
In the 50-60s, the development of this area in science is expressed in the appearance of phase diagrams of new polymer systems, in particular graft copolymers, but with the same known types of phase equilibria - amorphous and crystalline. But already in 1941, V.A. Kargin and G. L. Slonimsky suggested that the chain structure of macromolecules may be a prerequisite for the formation of LC phases by polymers. This assumption was developed in the works of R. L. Flory, who theoretically showed the inevitability of the appearance of an LC phase in solutions of rod-shaped macromolecules.
Experimental detection of such a phase state occurs at the end of the 60s, first in synthetic polypeptides (solutions of poly-γ-benzylglutamate), and then in fiber-forming polymer systems (solutions of para-aromatic rigid-chain polyamides). It is for these fiber-forming systems that S.P. Based on physicochemical, rheological, and structural data, Papkov was the first to propose a schematic phase diagram that takes into account the LC state in combination with amorphous and crystalline equilibrium. Today, it can rightly be called the "Papkov diagram" (Fig. 1).
Regarding the schematic nature of this diagram, questions immediately arise: why is it schematic? Is it good or bad?
The scheme in this case provides the versatility of its application to various polymers.
IOVLEVA, BANDURYAN
Rice. Fig. 1. Schematic generalized diagram of phase equilibrium in a rigid-chain aromatic polyamide-solvent system in the coordinates composition (polymer content in the x system)-temperature T. Curves are the boundaries between the phase regions: isotropic solution (IS), anisotropic solution (AR), crystal solvate (CS ), crystalline polymer (CP), polymer (P). Tu x*; T2 x**; T3 x*** - initial temperature-concentration parameters of phase transitions; xx is the polymer content in the CS.
nym systems in the form of separate fragments or even completely, which, obviously, is not bad. The numerical values of the boundaries of phase states are designated in accordance with the specific data of studies of specific polymer systems. Speaking of this, it should be noted that the scheme was born from fragmentary original data, since there was not and still is not any one general method for constructing complete phase diagrams of polymer systems. Having a complete, albeit schematic, phase diagram and based on information about the nature of a particular polymer system, it is possible to move from the general to the particular, namely, to identify the alleged specific fragments of the phase diagram.
It makes sense to explain the above reasoning of a general nature by the results of experimental studies. For example, the so-called corridor (Fig. 1, IR + AR) of the phase diagram of the poly-p-benzamide (PBA)-DMAA-100 system was clearly identified (its temperature-concentration boundaries were established) due to the fact that PBA solutions in DMAA-10 at certain concentrations and temperatures, like solutions of cellulose diacetate in chloroform, they can spontaneously separate into two phases. In particular, a 12% PBA solution spontaneously exfoliates into two layers after 4-5 days. If the solution is placed
schen in a graduated test tube, it is possible to monitor the change in the volumes of the layers in time. At some point, volumes stop changing. Then the polymer concentration in each layer is determined. Such experiments were carried out in the temperature range from -12 to +120°C. The results in the form of the dependence of the concentration of coexisting layers on temperature formed the corridor predicted in general form by Sh. Flory and indicated on the Papkov schematic diagram. Of course, the interpretation of these experiments was facilitated by the fact that there were already theoretical ideas and some actual data that PBA solutions can be in the LC state under certain conditions. The specific coordinates of the phase diagram corridor PBA-DMAA-100 turned out to be equal to from 0.06 to 0.10 volume fractions of the polymer in the temperature range set essentially by the freezing (-20°C) and boiling (+165°C) temperatures of the solvent.
The temperature-concentration coordinates of the corridor of another polymer system, poly-p-phenylene terephthalamide (PPTA)-H2O4, were elucidated in an original way when determining the viscosity properties of solutions in wide ranges of concentrations and temperatures. As in the case of PBA solutions, for PFTA-HNO4 solutions, we first obtained information about their LC state and that at the concentration of the transition from an isotropic solution to a liquid-crystal (anisotropic) viscosity, the viscosity sharply decreases, and then at a slightly higher concentration begins to increase quite sharply. These features of the viscosity properties of PPTA solutions in sulfuric acid made it possible to establish the quantitative boundaries of the phase diagram for this polymer system (Fig. 2).
On fig. 2, along with the corridor, one more boundary is marked (curve 3). It corresponds to the transformation of LC solutions into "solid" systems. The same boundary is also revealed in the PBA-DMAA-YU system. As shown by further studies involving XRD, the transformation of LC solutions of PBA, PFTA, and other para-aramids into "solid" systems can be due to the formation of crystal solvates (CS). They are undoubtedly associated with the crystalline phase state, but they are so specific that they can be the subject of separate consideration. Here, within the framework of the discussion of the actual schematic phase diagram, it should only be emphasized that CSs, nucleating in an isotropic or anisotropic solution and causing their transformation into "solid" systems, can coexist with each of these solutions. On the Papkov diagram (Fig. 1), this is reflected by the type designation IR + KS or AR + KS, indicating the two-phase sections.
PHASE EQUILIBRIUM IN POLYMER-SOLVENTER SYSTEMS
Rice. Fig. 2. Phase diagram of the PFTA-sulfuric acid system: 1, 2 - curves of the compositions of the coexisting isotropic phase (1) and LC phase (2); 3 - curve of the transition of the LC solution to the "solid" state.
Rice. Fig. 3. Dependence of the temperature T of a sharp change in turbidity on the concentration x of solutions of PPTA-sulfuric acid copolymer. The dashed lines are the boundaries between the phase regions.
Considering the issue of concretization of the Papkov schematic phase diagram, interesting data should be presented on the PFTA copolymer consisting of p-phenylene terephthalamide units and a small amount of benzimidazole units. This copolymer behaves similarly to PPTA in sulfuric acid solutions. Its solutions can turn into liquid crystal (anisotropic - AR) and solidify. When studying the light scattering of PFTA copolymer solutions in a wide range of concentrations and temperatures, it was noted that the integral turbidity of solidified solutions can change dramatically. On the plot of the dependence of the temperature of a sharp change in turbidity on the concentration of the solution (Fig. 3), an undeniable similarity with the contours of the main curves of the schematic phase diagram is easily detected. This fact convincingly confirms the validity of the generalized Papkov phase diagram, and for the PFTA-HN04 copolymer system, it makes it possible to specify the temperature-concentration boundaries of the diagram sections. According to this identification specification, the curve, located in the concentration range from 8 to 11-12% and covering the temperature range from 40 to 55°C, is the boundary between single-phase isotropic solutions and
There are several mechanisms for orienting macromolecules. In nature, the growth of cellulose (cotton, flax, hemp, jute, etc.) and protein (wool) fibers determines the longitudinal orientation of the macromolecules that form the fibrillar structure. In artificial and synthetic polymers, the orientation of macromolecules is determined by processing techniques. Orientation effects are most fully manifested in films and, especially, in fibers. The manufacturing technology of these products, as a rule, involves the extrusion (extrusion) of a polymer solution or melt through a calibrated hole of a certain shape - a die. Depending on the method of molding (melt, wet molding of the solution, dry-wet molding of the solution, dry molding of the solution), the orientation processes proceed differently. It is important to take into account that all structural changes in polymers occur in time and are relaxational. This manifests itself, for example, during phase transitions in a system at rest at different rates of temperature change or in structural transitions under the action of an external mechanical field. The role of structural-relaxation factors is most clearly manifested in the processes of "orientational structure formation", i.e. in the longitudinal flow of solutions and melts of crystallizing and amorphous polymers, non-isothermal crystallization in an external mechanical field and, in particular, in the process of the “jet-fiber” transformation. Already at the molding stage, with a longitudinal flow through the holes of the spinneret, the orientation of macromolecules along the fiber axis occurs. Molecular models of polymeric liquids when oriented in a jet are shown in Figs. eighteen.
Fig.18. Molecular models of polymeric liquids for orientation in a jet:
a – rigid ellipsoids; b – dilute solution of flexible chain macromolecules;
c – moving grid with local dissociating nodes.
However, for flexible-chain polymers, the orientation achieved at this stage is insufficient, especially since in the region of the exit from the die, relaxation proceeds so quickly that it practically negates the effect achieved in the die channel. The main orientation is created at the stage of hardening drawing, the value of which is the greater, the higher the stretching ratio. And the multiplicity of stretching depends on the temperature, duration (stretching speed) and drawing force. The stretching process is characterized by stretching curves under isothermal conditions (curves σ-ε). On fig. 19 shows the stretch curves of polyamide fibers at different temperatures. (M.P. Nosov in "Theory of formation of chemical fibers" M. Chemistry, 1975 p. 178)
Rice. 19. Stretch curves of polyamide fibers at different temperatures (in about C). 7 - -200; 6 - -170; 5 - -100; 4 - - 20; 3 - -15; 2 - +50; 1 - +75. The abscissa axis is not strength, but the pulling force (tension).
The maximum stretch, above which the strength begins to decrease, is achieved for different polymers at different temperatures inherent in a given polymer. In other words, it seems that for each polymer there is a technological limit to the stretching ratio and, accordingly, to the achievable strength value. This limitation encourages the development of special technological methods for increasing the stretching ratio. So, in 1964 Bondarenko V.M., Bychkov R.A. and Zverev M.P. was proposed "Method of single-stage drawing of synthetic fibers", which allows to increase the multiplicity of stretching and, accordingly, strength by drawing above the melting point of the polymer (A.S. No. 361234), which was achieved by stretching on special gradient heaters that provide a gradual increase in temperature (A.S. No. 347377). And in the 80s, “gel technology” was developed, which made it possible to achieve record strengths (see section 3).
In crystalline polymers, during stretching, the destruction (“melting”) of crystals occurs according to one of the possible mechanisms with the formation of a fibrillar structure by straightening macromolecules from several lamellae (Kaboyashi) and by gradually tilting the chains, sliding them over each other and disintegrating the crystal into separate blocks of folded chains (Peterlin). Crystal destruction schemes according to Kaboyashi (a) and Peterlin ( b) are shown in fig. twenty.
Fig.20. Molecular mechanism of plastic deformation of polymer crystals: a) according to Kobayashi: b) according to Peterlin.
The structure formed after deformation (stretching) undergoes further changes during heat treatment or the action of solvents. From a structural point of view, orientational secondary crystallization occurs here. In this case, the sizes of crystallites grow, and their order increases. However, such treatment may somewhat reduce the molecular orientation.
In rigid-chain polymers formed from a solution, the molecular orientation can be introduced at the stage of solution preparation. The fact is that some solutions of rigid-chain polymers can be in the liquid-crystalline state (in the mesophase). In contrast to low molecular weight liquid crystals, the mesogenicity of a polymer molecule is determined not by the length of the entire chain, but by the size of a statistical segment, the length of which is several hundred angstroms.
It has been established that the transition of rigid-chain polymers upon dissolution into an ordered state has the character of a first-order phase transition, in which a nematic-type structure appears. As the concentration increases, the viscosity of the solution increases, and when the critical concentration is reached, it drops sharply. At high shear stresses (mixing), the maximum does not appear and the solutions behave like ordinary isotropic ones. It follows from this that intense mixing prevents the formation of a liquid crystal structure.
The transition from an isotropic state to an anisotropic state is recorded:
a) polarization-optical and visual observations. Solutions become cloudy, sometimes opalescent;
b) rheological methods. The maximum viscosity corresponds to the point of inversion of an isotropic matrix with inclusions of areas of anisotropic formations into an anisotropic matrix with inclusions of isotropic areas. Fibers formed from anisotropic solutions are stronger than those formed from isotropic solutions. The crystallinity of fibers from anisotropic solutions is higher than from isotropic ones.
When the mesophase solution flows through the spinneret channel, nematic crystals are oriented along the fiber axis, which directly provides strength values of 2–4 GPa. The main type of supramolecular formations in these fibers are fibrils. The microfibril consists of crystallites and amorphous interlayers. Molecular chains in amorphous interlayers are almost parallel to the crystallite axes. Microfibrils are located along the fiber axis (some of them are at an angle of 10 0)
Not all heat-resistant rigid-chain heavy-duty fibers are crystalline. So, the fiber "vniivlon" is amorphous. What all superstrong fibers have in common is the number of molecular chains per unit fiber cross section. The number of through chains holding the load in the loaded sample is at least 0.75, and the orientation factor is at least 0.95.
"Rigidity" can be artificially imparted to flexible-chain polymers by the energy of an external field, i.e. stretch the macromolecules by a hydrodynamic or mechanical field, in which case a nematic structure may also arise.
In general, the strength of materials depends on the type of chemical bonds between the atoms of the material, on the structure of the material. There are theoretical, real and operational strength, i.e. the one that is included in the design calculations. Theoretical strength is calculated based on the magnitude of the forces of interatomic interaction that take place in a given material. For polymers, the calculation of theoretical strength is based on the assessment of the work of breaking macromolecules along the line of the main bonds of polymer chains. It is assumed that, in the ideal case, the macromolecules are densely packed and their axes are located strictly along the direction of the tensile force. In this case, the length of the molecules is considered as infinitely large, i.e. rupture occurs simultaneously for all macromolecules per cross section of the sample. Calculations show that at absolute zero temperature the strengths are close to 6–8 GPa.
With increasing temperature, the strength decreases and at 25 0 C (298 0 K) it is 0.55 - 0.65 of the theoretical one. The values of the real strength of many polymers have reached, and sometimes even exceed, theoretical calculations. This is probably due to the contribution of intermolecular interaction forces, which are not taken into account in the theoretical calculation. It is clear that the greatest strengths are achieved for oriented materials when as many bonds as possible fall into the fracture cross section. The orientation measure is taken to be the misorientation angle a, which is the angle between the fiber axis and the average orientation angle of the macromolecules. On fig. 21 shows the dependence of the relative strength s /s theor. from misorientation angle a. As can be seen from fig. 21, when the misorientation angle decreases to 30 0 , i.e. to the state that corresponds to the fibers that came out of the precipitation bath and not subjected to additional high orientation stretching, the relative strength is less than 0.1 of the maximum strength of a perfectly oriented fiber. Then, as the misorientation angle decreases, the strength begins to increase sharply. At a misorientation angle of 8 0, the strength is half of the maximum strength, i.e. 2500 MPa. In fact, with this orientation, a strength of no more than 1000 MPa is achieved. The reason for this discrepancy is the imperfection of the macro- and microstructure of the fibers. It, in turn, depends on the molding conditions that determine the kinetics and mechanism of phase separation in the event of an imbalance in the polymer–solvent systems.
0,5 Fig.21. Relative dependency
strength from the misorientation angle.
