Issue 1

A unique feature of gradient materials is a gradual change of their properties from a soft rubber to a glassy polymer within one and the same product (sample). Such a control of the hardness, the elasticity modulus and other physico-mechanical characteristics can be achieved only owing to the directed changes in the chemical structure of a polymer matrix during its synthesis, without recourse to the conventional methods for polymer modification or the manual methods for creation of composite structures, such as welding, gluing, or mechanical assembling.

A possibility of production of these materials was predicted theoretically [1–5]. In particular, the material structure must be formed as a dense network containing bulky rigid cross-links connected by flexible chains with controllable lengths. This follows from a generalized equation for evaluation of the equilibrium rubber elasticity modulus E_∞ for network systems, which was derived and described in references [1–5]:

     (1)

where E₀ is the elasticity modulus of a network polymer for which the distance between the network cross-links is comprised by a single repeating unit,

      (2)

m is the number of repeating units in an average fragment between cross-linked points; Ф is the network functionality (the number of chains branching from a cross-link); ρ is the density; R is the universal gas constant; Т is the temperature; and М₀ is the molecular mass of the repeating unit in this fragment. The value of β represents the ratio of the van der Waals volume of the network cross-link    to the van der Waals volume of the repeating unit of a linear fragment    

     (3)

The notion of a network cross-link from the considered viewpoint is described in detail in the above-mentioned references. The network cross-link is a group of atoms which includes an atom serving as a branching center and adjacent chemically bound atoms with their closest substituents.

It can be readily shown that, taking into account formulae (2) and (3), relation (1) goes over into the following equation

      (4)

or     (5)

where M_c is the average molecular mass of the linear fragment between ajasent network cross-links.

If the network is coarse, then M_c >> M₀ and b/m << 1. Under such conditions, equations (4) and (5) go over into the following classical relation

              (6)

For dense networks, when the distance between adjacent cross-links is equal only to several repeating units or is even shorter than a single unit, the value of β assumes the key role, since М_с ~ М₀ and m ~ 1. If the process of microphase separation is controlled so that the bulky polar network cross-links form microdomains due to a drastic change of their surface energy from that of the flexible and short nonpolar chains, then these microdomains can serve as network cross-links. In this case the van der Waals volume of these cross-links, , will essentially exceed that of the repeating unit in the fragments between cross-linked points, , and the value of β, according to equation (3), will acquire higher magnitudes which will lead to the enhanced values of E_∞ according to equations (4) and (5).

Hence, the higher value of E_∞ can be achieved on passing to the dense networks with bulky cross-links, when М_с ~ М₀, m ~ 1 and  >   . It is very important that the elasticity moduli can take on the high values despite the fact the glass-transition point of a polymer network still remains low. This principle was realized in a multitude of works [6–11] by the synthesis of poly(urethane isocyanurate) networks via the reaction of polycyclotrimerization.

It was mentioned earlier that the production of gradient materials based on network poly(urethane isocyanurates) is a convenient model for realization of their synthesis in an automatic mode using programmed algorithms. Herein we present the results on investigation of the materials obtained on a unit with programmed control of the speed of feeding of material components into a blender. Their gradient structures were confirmed using different physical methods. The properties of the resulting materials were compared to the characteristics of the samples synthesized by the conventional method.

Results and discussion

The samples of the materials obtained on a modified unit do not contain microscopic defects on the surface, are monolithic and uniform, and possess well reproducible properties. Strict control of the speed of feeding of the composition components into a blender allowed us to overcome the drawbacks incident to the samples obtained upon manual control of this parameter of the gradient material synthesis.

Previously it was demonstrated that the gradient material based on PPG-2000 and 2,4-TDI has a network structure, where the bulky network cross-links are formed by the aggregates from isocyanurate rings and the flexible fragments between cross-linked points consist of the poly(propylene glycol) chains. Since the isocyanurate rings possess considerably higher surface energy (γ = 56.8 mN/m) than PPG-2000 chains (γ = 27.3 mN/m), the material undergoes microseparation. Its gradient structure is formed by a monotonous change of the number of bulky cross-links in a network structure along the given direction.

Figure 1 shows the stress–strain curves of the samples cut from different zones of the material macrosample according to the diagram presented in Fig. 2. As the content of 2,4-TDI in the composition of a reaction mixture increases and, as a consequence, the content of isocyanurate fragments in a chemical structure of the material grows, there is observed an improvement in the strength characteristics of the microsamples and a change in the form of stress–strain curves. At the minimal content of 2,4-TDI (zones 1, 2), they resemble the stress–strain curves of soft rubbers – the stress monotonously increases with a strain growth. Upon further increase in the concentration of the isocyanurate fragments, the form of the stress–strain curves becomes more typical for rigid rubbers, namely, the stress–strain curves of the samples can be conventionally divided into two regions with essentially different rates of stress growth upon increase of strain ε. The first region before ε ≤ 5% corresponds to elastic behavior of the sample; there is observed a linear growth of the stress with a strain rise. Upon further deformation of the sample, the rate of stress growth in it reduces and monotonously increases with a growth in the strain, which is characteristic of dense polymers upon realization in them of rubbery properties. Figure 1b shows the dependence of the stress difference at 30 and 5% deformation of the samples depending on the macrosample length. As the content of the isocyanurate fragments in the material structure increases, the rate of the stress growth in this range of strains firstly increases and then slightly changes while approaching the zones with their highest concentration.

Figure 1. Stress–strain curves of the samples (a) cut from sections 1 (1), 3 (2), 5 (3), 7 (4), and 9 (5) and the dependence of the stress difference at 5 and 30% deformation on the macrosample length (b). The location diagram for the considered macrosample zones is presented in Fig. 2.

Figure 2. Diagram of cutting of microsamples from the monolithic gradient material. An arrow shows the direction of the growth of 2,4-TDI content in the material sample.

Figure 3 depicts the dependence of the elasticity modulus E on the macrosample length (or an increase in the concentration of the bulky network cross-links). The values of E monotonously increase along the macrosample length as the concentration of 2,4-TDI in the reaction mixture grows. The experimental values of the elasticity modulus fall well on a single dependence which equation has the following form:

E = 64.82 + 34.73l – 1.24l² + 0.24l³                       (7)

The resulting analytical equation is convenient to use for evaluation of a range of elasticity modulus variation along the macrosample length. According to relation (7), the value of E at l ≈ 0 and l ≈ 15 cm increase in 17 times and compose 65 and 1106 MPa, respectively.

For comparison Fig. 3 shows the values of E for the microsamples cut from the macrosample obtained upon manual control of the speed of feeding of the mixture components [12]. Comparing the experimental values of the elasticity moduli of two gradient materials, one can note that the automatic control of the speed of feeding of the mixture components affords a gradual change of the elasticity moduli of the gradient material, which fall on a single curve. The manual control of the mixing process leads to a number of rises and falls in the elastic modulus growth, which indicates the violation of a monotonous change in the concentration of the isocyanurate fragments along the length of the resulting gradient material.

Figure 4 shows the values of the Brinell hardness number H_B in different zones of the macrosample. The values of H_B, as well as those of the elasticity modulus, monotonously increase with a growth in the content of the isocyanurate fragments along the sample length. For convenience of comparison, Fig. 5 presents the dependences of H_B and E in the same coordinates. As the elastic modulus of the material increases, the rigidity of the microsamples also grows.

Figure 3. Dependence of the elasticity modulus on the length of the gradient material sample: 1 – material obtained on a modified unit; 2 – material obtained on a unit with manual control of the speed of precursor outflow [12].

Figure 4. Dependence of the Brinell hardness number on the length of the gradient sample. The loads on the sample were equal to 5 kg (1), 10 kg (2), and 15 kg (3).

Figure 5. Change in the Brinell hardness number at the load of 15 kg and change in the elasticity modulus of the material depending on the macrosample length: 1 – dependence of H_B, 2 – dependence of E.

The values of the Brinell hardness number of the material were measured at three different loads. As can be seen from the results presented in Fig. 4, an increase in the elasticity modulus affords a growth in the difference of the values of H_B measured at different static loads. This is connected with a nonlinear mechanical behavior of the high-modulus polymer material, when the parameters of a relaxation process are not constant and depend on the mechanical load or deformation.

The dynamic mechanical characteristics (storage modulus G', loss modulus G", mechanical loss tangent tgd) were determined using two samples cut from different regions of the gradient material. The first sample with the length of 6 cm and the width of 1 cm contained sections 1–4 of the macrosample (Fig. 2). The elasticity modulus in it, according to equation (7), smoothly changed from 65 to 280 MPa. The second sample with the same sizes included sections 5–8, and its elasticity modulus changed from 280 to 712 MPa.

The dependences of moduli G' and G" and tgd on the temperature are demonstrated in Fig. 6. It is obvious that the storage modulus at the temperatures up to –60 °С takes on the high values equal to 1740 MPa. This is associated with the fact that in this temperature range the polymer is in a glassy state. Upon temperature rise from –60 to 150 °С, the storage modulus gradually reduces; at the same time, the storage modulus G' for the sample with the high values of Е is essentially higher (curve 2) than that for the more low-modulus one (curve 1).

The temperature dependence of tgd shows the presence of two maxima (Fig. 6c). An unsymmetrical shape of each of the maxima is caused by the gradient structure of the material, i.e., the elasticity modulus of the samples is not a constant value and monotonously grows along their length. The first maximum is observed at the temperature of –38 °С. Its temperature is the same both for the high-modulus sample and for the low-modulus one and corresponds to devitrification of the fragments between cross-linked points. According to the results of calculation of the glass-transition points of linear fragments between cross-linked points of the material, which consist of poly(propylene glycol) chains, it is equal to –45 °С and is close to its experimental value. The calculation was performed using a Cascade program according to the following equation [2–5]

                 (8)

where  is the van der Waals volume of the repeating unit; a_i are the atomic constants connected with the energy of weak dispersion interaction, b_j are the constants connected with the energy of strong intermolecular interaction (dipole–dipole interaction, hydrogen bonds); and ΔV_i is the van der Waals volume of i atom.