The state of single-component systems is determined by two independent variables: pressure and temperature.
The number of degrees of freedom of an equilibrium thermodynamic system, which is affected only by temperature and pressure, is equal to the number of components of the system minus the number of phases plus 2, i.e. S = k – f + 2 (according to the Gibbs phase rule).
In a one-component system, three phases can exist simultaneously: solid, liquid and vapor, and the following two-phase equilibria are possible:
1) liquid phase – solid phase
2) liquid phase - steam
3) solid phase - steam
Each of these equilibria is characterized by a certain curve P = f(T). The position of the curves is determined by the Clapeyron–Clausius equation:
Graphic representation of the state of equilibrium phases at different temperatures and pressures called state diagram .
The state of the system is represented by a part of the plane called phase field .
Phase field– geometric locus of points representing different states of the same phase.
Phase fields are separated by phase lines.
Water diagram
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Figure 3. Diagram of the state of water
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The number of degrees of freedom at this point is determined by the formula S = k – f + 2 = 1 – 3 + 2 = 0.
If you change one of the variables at this point, one of the phases will disappear. For example, if you increase the temperature, the solid phase will disappear. As long as the solid phase disappears, the temperature will not change.
After the disappearance of the solid phase, a two-phase liquid-vapor system will remain. It is monovariant i.e. S = 1 – 2 + 2 = 1.
Therefore, it is represented by a phase line.
Line OS displays the liquid-vapor equilibrium. In this system, you can change either the pressure or the temperature. If you increase the temperature, the pressure will increase and the figurative point will move up the curve OS. Dot WITH- this is the critical point above which the liquid cannot exist, because T = 647.35 K; P = 221.406 Pa.
Line OS you can continue in the opposite direction beyond the triple point ABOUT(line OD). It corresponds to the equilibrium of vapor - supercooled liquid, i.e. shows the vapor pressure above supercooled water. It is always higher than the vapor pressure above the ice. Therefore, supercooled water is an unstable (metastable) phase relative to ice, which is stable in this temperature range.
When the temperature drops (at the point ABOUT) the liquid disappears. The system will become two-phase: ice - steam, monovariant (curve JSC). Line OB corresponds to the melting (or crystallization) curve.
The number of degrees of freedom at any point belonging to any phase line reflecting two-phase equilibrium is equal to 1, i.e. S = 1 – 2 + 2 = 1.
This means that in order for the system to maintain equilibrium, only one of the parameters can be changed (either temperature or pressure).
The dependence of pressure on temperature is described by the Clausius–Clapeyron equation.
Let's consider specific cases of its application.
A) Equilibrium liquid vapor; DH use > 0,
Then 
Since the specific molar volume of vapor is greater than the corresponding volume of liquid, i.e. V p >V f, which means it is always positive. Consequently, the evaporation temperature always increases with increasing pressure. The value reflects the slope of the curve and shows the change in temperature with increasing pressure.
B) Equilibrium solid-liquid; DN pl (curve OB)
; DV = (Vf – Vtv) – very small
Consequently, the solid-liquid equilibrium curve is also very large ( OB) goes up steeply.
It should be noted that for substances such as water, bismuth, gallium in the solid state, their density is less than in the cooled state.
For them V f >V tv, i.e. V f – V tv< 0
Therefore, the derivative is negative and the melting curve is inclined slightly to the left.
Sulfur phase diagram
In one-component systems there can only be one steam and one liquid phase, and there may be several solid phases. Sulfur, for example, has two modifications: rhombic S rhombus and monoclinic S monocle(Figure 4).
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Rice. 4. State diagram of sulfur
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When ordinary sulfur is heated above 95.5 0 C, it gradually turns into monoclinic S monocle
Thus, the number of possible phases for sulfur is 4: orthorhombic (solid), monoclinic (solid), liquid and vapor.
Solid lines divide the diagram into four areas:
area above DAVE– single-phase region of orthorhombic solid sulfur;
ABC– single-phase region of solid monoclinic sulfur;
EBCF– single-phase region of sulfur in the liquid state;
area below DASF– single-phase region of vaporous sulfur.
Each curve of this diagram reflects the corresponding phase equilibria:
AB – S rhombus S monocle
BC – S monocle S liquid
AC – S monocle S pair
AD – S rhombus S pairs
BE – S rhombus S liquid
CF – S liquid S steam
At point A: S rhombus S monocle S pairs
B: S diamond S monocle S liquid
C: S monocle S liquid S steam
The number of degrees of freedom at these points is 0: S = 1 – 3 + 2 = 0
The supposed fourth point corresponding to equilibrium
S monocle S liquid S steam
practically difficult to implement, because This equilibrium is metastable.
Equilibrium of all four phases
S rhombus S monocle S liquid S steam
cannot be feasible under any conditions, because the phase rule for this equilibrium leads to a negative number of degrees of freedom:
S = 1 – 4 + 2 = – 1
So, when heated, sulfur can transform from orthorhombic to monoclinic. The reverse process is also possible, i.e. upon cooling, the transition of sulfur from monoclinic to orthorhombic S monocle S rhombus.
Thus, the mutual transformation of one crystalline form of sulfur into another occurs reversibly.
If a given modification of a crystalline substance has the property, when external conditions (for example, temperature) change, to transform into another modification and, when the previous conditions are restored, to return to the original modification, then such polymorphic transformations are called enantiotropic ).
An example of an enantiotropic phase transition is the process of mutual transition of orthorhombic sulfur and monoclinic sulfur.
Transformations of modifications that can occur in one direction are called monotropic (benzophenone).
Two-component systems
When studying systems consisting of two components, the method of graphically depicting the dependence of any property of a solution on its concentration is used.
This graphical representation is called a composition-property diagram.
Typically, the diagram should fit on a plane limited by the ordinate and abscissa axes (Figure 5).
Rice. 5. Diagram composition - property
Any property (temperature, pressure, density, refractive index, etc.) is plotted on the ordinate axis.
The composition of the binary mixture is plotted on the abscissa axis, which can be expressed in mole fractions or percentages.
Left point A corresponds to 100% content of component A, right point IN corresponds to 100% content of component B. Intermediate points between A and B correspond to mixtures consisting of two components. As you move away from the point A the content of component A decreases, but the content of component B increases.
Entropy of mixing for a 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 less because the monomer units of the polymer are not able to fully utilize the increase in volume upon mixing. This is prevented by the “connectedness” of the monomers in the polymer. And the energy of mixing has the same form as for a mixture of two low molecular weight liquids.
Consider a solution consisting of N solvent molecules and N2 polymer molecules with degree of polymerization g; 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 the expression
Rice. 4.
The energy of mixing 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 denote this difference AAS:
Thus, the value A.A.S. increases with the length of the polymer molecule, and, as a consequence, it can be expected that the phase separation of a 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, the free energy of mixing per mole can be expressed by the equation where the first term represents the change in energy and the second term represents 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 a binary solution:
Rice. 5.
A nonmonotonic change in the chemical potential indicates 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 critical parameters for polymer solutions with the corresponding parameters for regular solutions x c = 2ifs = 0.5. It can be seen that polymer solutions more easily become incompatible and separate into phases).
I-Temperature
In polymer science, the concept of i-temperature and the concept of good and bad solvents are widespread. To introduce these concepts, let's return to the equation. The excess chemical potential for small volume fractions of a solute can be expanded into the following 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 - the solvent is bad. 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 is observed:
Rice. 6.
Thus, from the equation, the u-temperature can be defined as the critical temperature for an infinitely long polymer.
RHEOLOGY– the science of deformation 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 load-induced stresses exceed a known value - the yield strength; they persist after the load is removed; viscous flow is distinguished by the fact that it occurs at any arbitrarily small stresses; with increasing stresses, the flow speed increases, and if the stresses are maintained, the viscous flow continues indefinitely. Another property that media studied by rheology may have is high elasticity, characteristic, for example, of rubber, when a rubber band can be stretched tenfold, and after removing the load it 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 detected. Rheological phenomena manifest themselves in many natural processes and in a large number of technological ones. There are very numerous substances involved in such processes: these are rocks that make up the earth’s crust, magma, volcanic lava, oil and clay solutions that play a vital 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, this is bread dough and dough-like masses from which candies, sausages, creams, ointments, toothpastes are made, this is solid fuel for rockets; These are, finally, protein bodies, for example, muscle tissue.
THERMODYNAMICS OF SPONTANEOUS DISSOLUTION OF POLYMERS
The dissolution of polymers is analogous to the unlimited mixing of two liquids, subject to the second law of thermodynamics. The second law of thermodynamics is a general law that allows one to find the direction and establish the possibility or impossibility of thermodynamic processes occurring. According to the second law, heat cannot spontaneously transfer from a less warm body to a warmer one.
Processes in which thermal phenomena are involved spontaneously proceed in only one direction and stop after a 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 processes are possible in which 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 enthalpy of mixing; ΔS - change in entropy, or entropy of mixing; T - 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 - heat is not absorbed or released (athermic dissolution).
Compliance with the thermodynamic dissolution condition ΔG<0 возможно при следующих условиях:
1) subject to Δ N< 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) provided Δ S> 0, which always occurs in practice during dissolution, since the entropy of mixing is always positive. The entropy of mixing of BMC with a solvent, calculated per weight fraction of the substance, lies between the values of the entropy of dissolution of low-molecular substances and typical colloidal systems.
Often, when dissolving an IUD, the dissolution process occurs solely due to a change in entropy (increasing), i.e., athermic. The influence of temperature should also be taken into account. If at a certain temperature the polymer does not dissolve (ΔН-TΔS>0), then with increasing temperature the absolute value of TΔS may become greater than the absolute value of ΔН and then the sign of the inequality 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 unlimited mixing of two liquids, has a number of disadvantages due to many assumptions and corrections in determining both the entropy of mixing ΔS and the heat of mixing ΔH of the polymer with the 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 and depends on their chemical composition and structure, external conditions, in particular on temperature. The basic law of equilibrium of a multiphase multicomponent system is the Gibbs phase rule, which establishes the relationship between the number of phases Ф, 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, i.e., without disturbing its equilibrium.
In systems in which the components are only in liquid and solid states, changes in pressure have little effect on the properties, so the pressure can be considered constant, and the phase rule equation 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 a certain temperature, these phases can merge to form a single-phase homogeneous solution. On the contrary, a single-phase homogeneous solution at a certain temperature can stratify or separate into two phases. The temperature at which separation occurs is called the phase separation or phase separation temperature (PST). A solution of each concentration has its own GfR, the dependence of which on the composition of the solution is expressed by a mutual mixing curve, or a boundary curve separating the region of single-phase solutions from two-phase ones.
Depending on the composition of single-phase two-component liquid solutions when they are cooled, two cases of separation into component components are possible: liquid and crystalline. With liquid separation, one liquid phase separates into two liquid phases; with crystalline separation, a component in the form of a crystalline phase is released from the solution.
HIGH MOLECULAR COMPOUNDS, 2010, volume 52, no. 11, p. 2033-2037
UDC 541.64:536.6
PHASE EQUILIBRIA IN POLYMER-SOLVENT SYSTEMS:
DEVELOPMENT IN FIBER
© 2010 M. M. Iovleva, S. I. Banduryan
Limited Liability Company "LIRSOT" 141009 Mytishchi, Moscow region, st. Kolontsova, 5
A brief overview 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. Papkova in the creation and development of scientific ideas about phase equilibria in fiber-forming polymers with the participation of solvents.
The history of the systematic study of phase equilibria in systems including fiber-forming polymers goes 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, observations of the unusual behavior of cellulose diacetate solutions depending on 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 either a true single-phase solution or two liquid phases in equilibrium in water in different temperature and concentration regions. These studies of solutions of diacetate and other cellulose ethers, in particular nitrates, began at the Research Institute of Artificial Fiber (Mytishchi). In 1937, a widely known article by S.P. was published. Papkova, V.A. Kargina, Z.A. Rogovin, in which for the first time a polymer-solvent phase diagram was constructed and conclusions were drawn about the possibility of polymers forming not only colloidal, but also molecularly dispersed solutions.
To these results, which have become textbook, it should be added that in the same years, research began on ternary polymer-solvent-precipitant systems, described, as a rule, using the plane of a triangle. Work in that period was related only to amorphous equilibria. But soon they initiated research into solutions of a highly crystallizing 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 twentieth century, the formation of the doctrine of phase equilibria in systems of amorphous and crystallizing, and mainly fiber-forming, polymers took place.
In the 50-60s, the development of this direction 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 the LC phase in solutions of rod-shaped macromolecules.
Experimental discovery of such a phase state occurred in the late 60s, first in synthetic polypeptides (solutions of poly-y-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. Papkov, on the basis of physicochemical, rheological and structural data, 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 a “Papkov diagram” (Fig. 1).
Regarding the schematic nature of this diagram, questions immediately arise: why schematic? Is it good or bad?
The scheme in this case ensures the versatility of its application to various polymers.
IOVLEVA, BANDURYAN
Rice. 1. Schematic generalized phase equilibrium diagram in the rigid-chain aromatic polyamide-solvent system in the coordinates composition (polymer content in the system x) - temperature T. Curves are the boundaries between 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.
ny systems in the form of separate fragments or even completely, which is obviously not bad. Numerical values of the boundaries of phase states are designated in accordance with specific data from studies of specific polymer systems. Speaking of this, it should be noted that the scheme was born from fragmentary original data, since there was and still is not any one general technique 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 specific, namely, to identify the supposed specific fragments of the phase diagram.
It makes sense to explain the above general considerations with 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-SiO system was clearly identified (its temperature-concentration boundaries were established) due to the fact that solutions of PBA in DMAA-SiO 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 separates into two layers after 4-5 days. If the solution is placed
pchen in a graduated test tube, you can monitor the change in the volumes of the layers over time. At some point the 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 a dependence of the concentration of coexisting layers on temperature formed a corridor, predicted in general form by Sh. Flory and indicated on Papkov’s 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 of PBA-DMAA-YiO turned out to be equal to from 0.06 to 0.10 volume fractions of the polymer in the temperature range essentially specified 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-n-phenylene terephthalamide (PPTA)-H^O4, were clarified 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-H^04 solutions, information was first obtained about their liquid crystal state and that at the concentration of the transition of an isotropic solution to a liquid crystalline (anisotropic) viscosity sharply decreases, and then at a slightly higher concentrations begin 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).
In Fig. 2, along with the corridor, another border is indicated (curve 3). It corresponds to the transformation of LC solutions into “solid” systems. The same boundary is revealed in the PBA-DMAA-JU system. As further studies using X-ray diffraction analysis have shown, the transformation of LC solutions of PBA, PPTA and other para-aramids into “solid” systems may be due to the formation of crystal solvates (CS). They are undoubtedly associated with the crystalline phase state, but have such great specificity that they can be the subject of separate consideration. Here, in the framework of the discussion of the schematic phase diagram itself, 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 two-phase sections.
PHASE EQUILIBRIA IN POLYMER-SOLVENT SYSTEMS
Rice. 2. Phase diagram of the PFTA-sulfuric acid system: 1, 2 - composition curves of the coexisting isotropic phase (1) and LC phase (2); 3 - curve of transition of an LC solution to a “solid” state.
Rice. 3. Dependence of the temperature T of a sharp change in turbidity on the concentration of x solutions of the PFTA copolymer-sulfuric acid. Dashed lines are the boundaries between phase regions.
Considering the issue of specifying the schematic Papkov phase diagram, interesting data should be presented regarding the PPTA 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 crystalline (anisotropic - AR) and harden. When studying the light scattering of PFTA copolymer solutions in a wide range of concentrations and temperatures, it was noticed that the integral turbidity of solidified solutions can change sharply. The graph of the dependence of the temperature of a sharp change in turbidity on the concentration of the solution (Fig. 3) easily reveals an undoubted similarity with the contours of the main curves of the schematic phase diagram. This fact convincingly confirms the validity of the generalized Papkov phase diagram, and for the system the PFTA-H^O4 copolymer 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 macromolecules that form a fibrillar structure. In artificial and synthetic polymers, the orientation of macromolecules is determined by technological processing methods. Orientation effects are most fully manifested in films and, especially, in fibers. The technology for manufacturing these products, as a rule, involves extrusion (extrusion) of a solution or melt of polymer through a calibrated hole of a certain shape - a die. Depending on the molding method (melt, wet solution spinning, dry-wet solution spinning, dry solution spinning), the orientation processes proceed differently. It is important to take into account that all structural changes in polymers occur over time and are relaxation. This manifests itself, for example, during phase transitions in a quiescent system at different rates of temperature change or in structural transitions under the influence of an external mechanical field. The role of structural-relaxation factors is most clearly manifested in the processes of “orientation structure formation”, i.e. during the longitudinal flow of solutions and melts of crystallizing and amorphous polymers, non-isothermal crystallization in an external mechanical field and, in particular, during the “jet-fiber” transformation process. Already at the spinning stage, during longitudinal flow through the holes of the spinneret, macromolecules are oriented along the fiber axis. Molecular models of polymer liquids during orientation in a jet are presented in Fig. 18.
Fig. 18. Molecular models of polymer liquids during orientation in a jet:
a – rigid ellipsoids; b – dilute solution of flexible chain macromolecules;
c – moving mesh 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 the relaxation proceeds so quickly that it practically negates the effect achieved in the die channel. The main orientation is created at the stage of strengthening drawing, the magnitude of which is greater, the higher the drawing ratio. And the multiplicity of drawing depends on the temperature, duration (pulling speed) and drawing force. The drawing process is characterized by stretching curves under isothermal conditions (σ-ε curves). In Fig. Figure 19 shows the tensile curves of polyamide fibers at different temperatures. (M.P. Nosov in “The Theory of Formation of Chemical Fibers” M. Chemistry, 1975 p. 178)
Rice. 19. Tensile curves of polyamide fibers at different temperatures (in o C). 7 – -200; 6 – -170; 5 – -100; 4 – - 20; 3 - -15; 2 - +50; 1 - +75. The x-axis is not strength, but 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 expansion ratio and, accordingly, to the achievable strength value. This limitation encourages the development of special technological methods for increasing the multiplicity of stretching. So, in 1964 Bondarenko V.M., Bychkov R.A. and Zverev M.P. a “Method for single-stage drawing of synthetic fibers” was proposed, which allows increasing the drawing ratio and, accordingly, strength by drawing above the melting point of the polymer (A.S. No. 361234), which was achieved by drawing on special gradient heaters that ensure 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, when stretched, the destruction (“melting”) of the crystals occurs according to one of the possible mechanisms with the formation of a fibrillar structure by straightening macromolecules from several lamellas (Kaboyashi) and by gradually tilting the chains, their sliding over each other and the disintegration of the crystal into separate blocks of folded chains (Peterlin). Schemes of crystal destruction according to Kaboyashi (a) and Peterlin ( b) are presented in Fig. 20.
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. At the same time, the crystallite sizes increase and their ordering increases. However, such processing may reduce the molecular orientation somewhat.
In rigid-chain polymers formed from a solution, the molecular orientation can be established at the stage of solution preparation. The fact is that some solutions of rigid-chain polymers can be in a 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 to an ordered state upon dissolution 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 a critical concentration is reached, it drops sharply. At high shear stresses (stirring), the maximum does not appear and the solutions behave like ordinary isotropic ones. It follows that intensive stirring 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 the isotropic matrix with inclusions of regions of anisotropic formations in the anisotropic matrix with the inclusion of isotropic regions. Fibers spun from anisotropic solutions are stronger than those spun from isotropic solutions. The crystallinity of fibers from anisotropic solutions is higher than from isotropic ones.
When a mesophase solution flows through the die 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 layers. Molecular chains in amorphous interlayers are almost parallel to the axes of crystallites. Microfibrils are located along the fiber axis (some of them are at an angle of 10 0)
Not all heat-resistant rigid-chain super-strength fibers are crystalline. Thus, “vniivlon” fiber is amorphous. What all super-strong fibers have in common is the number of molecular chains per unit cross-section of the fiber. The number of pass-through chains holding the load in a 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 macromolecules by a hydrodynamic or mechanical field, and a nematic structure can also arise.
In general, the strength of materials depends on the type of chemical bonds between the atoms of the material and on the structure of the material. There are theoretical, real and operational strength, i.e. the one that is included in structural calculations. Theoretical strength is calculated based on the magnitude of the interatomic interaction forces occurring in a given material. For polymers, the calculation of theoretical strength is based on an assessment of the work of breaking macromolecules along the main bonds of the polymer chains. It is assumed that, in an ideal case, macromolecules are tightly 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 of all macromolecules per cross section of the sample. Calculations show that at absolute zero temperatures 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 value. The real strength values of many polymers have reached and sometimes exceed theoretical calculations. This is probably due to the contribution of intermolecular interaction forces that 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 section. The measure of orientation is the misorientation angle a - the angle between the fiber axis and the average orientation angle of the macromolecules. In Fig. Figure 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 corresponding to the fibers that came out of the precipitation bath and were not subjected to additional high orientation drawing, the relative strength is less than 0.1 of the maximum strength of an ideally 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 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 defective macro- and microstructure of the fibers. It, in turn, depends on the molding conditions that determine the kinetics and mechanism of phase separation when equilibrium is disturbed in polymer-solvent systems.
0,5 Fig.21. Dependency relative
strength on the misorientation angle.