FORMATION OF POLYURETHANE STRUCTURE
The chemical reactions that lead from reactants (isocyanates, chain extenders, polyols) to polyurethane polymer have been covered in detail in Chapter 3. The hard segment blocks are a result of isocyanate-chain extender reactions. The chain extender can be low-molecular weight polyols, polyamines, or water.
The first and third reactions are first order in each reactant, while the second reaction is first order in water and second order in isocyanate. Each reaction has a rate constant characteristic of the particular reactants and mutual solubilities which evolve as the reaction proceeds and heat of reaction is released. Soft segments are typically low polydispersity polyalkylene glycols (Mw/Mn ~ 1) or polyesters of polydispersity of about 2.0 made separately from the polyurethane polymerization.
It has been proposed that polyurethane structure from these reactions results in a block copolymer (Fig. 4.1) which can be treated using models for block copolymers [1-3] derived for well characterized or ideal block copolymer structures [4-7] Structures developed from a basis of ideal conditions usually begin from assumptions that the structure under consideration is fully phase separated and at a point of lowest free energy. Furthermore, these thermodynamic structures are often comprised of polymers having ideal polydispersity (i.e., Mw/Mn = 1) in their molecular weight as well in block size.
Addition polymers such as polyurethanes can never have these attributes and by nature of their chain growth process will have polydispersities from about 2.0 to the undefined dispersity of a thermoset. This issue of nonideal polydispersity of polyurethanes versus that employed to simplify theoretical calculation should not deter us,
FIGURE 4.1 Hard and soft polyurethane segments make for a multi-block copolymer.
Figure 4.2 Representations of polyurethane final structures. On the left is an idealized structure showing monodisperse hard segment lengths and block sizes isotropically dispersed in a monodisperse soft segment. On the right is a more realistic representation showing polydisperse hard segment lengths and block sizes, along with unassociated hard segments dissolved in the soft segment.
however, since the effect of polydispersity can be anticipated and should not deny us the insights such an analysis can provide. An additional problem is the equilibrium assumption which means that there is an expectation that the theoretical analysis is performed on a structure that is in the lowest energy state. Actual polyurethane structure reflects the thermodynamics of the polymer chains coming to an equilibrium structure convoluted with the kinetic limitations of a system that may be coming to a non-equilibrium state as a result of a cooling rate that is not infinitely slow (Fig. 4.2). Again, such considerations will apply to all real block copolymers that phase separate either upon cooling from a melt or assembling from a dilute condition. These variances of polyurethane reality from model assumptions should not prevent us from obtaining a good qualitative understanding of our systems both in how close or how far they lie from ideal expectations.
Figure 4.2 expresses final conditions in which hard segment is separated or partially phase separated from the soft segment. However, the path from the initial conditions to a final state represented by Figure 4.2 is dependent on several factors including the thermodynamic incompatibility of the hard and soft phases. Analysis of phase separation in block copolymer systems can be treated in limits of very strong phase segregation  or weaker phase separation [4, 6, 7]. The strong and weak limits are essentially indications of how much the phases mix even when they have achieved a phase-separated state such that each phase has more (weak segregation) or less (strong segregation) solubility in the other phase at equilibrium. Closer to the case for polyurethanes, Benoit and Hadiiaouannou  covered the case for block copolymers that are multiblock rather than simple diblock or triblock copolymers for instance. This matches polyurethanes in that over the course of a typical polymer chain, there may be many runs of hard and soft segment in sequence. Also cogent to polyurethane discussion is the work of Fredrickson and Helfand  in which polydispersity of molecular weights is included. A more recent treatment by Ginzburg et al.  has considered the structures created under moderate phase separation relevant to polyurethanes. In a situation of strong phase separation, the interfacial thickness between phases (see Section 188.8.131.52) is much less than the spacing between phase periodicity.
The force driving phase separation is phase incompatibility . The usual case is for two blended polymers to phase separate into macrophase-separated structures. A typical macrophase-separated structure between two immiscible polymers (in this case polydimethylsiloxane and polymethylmethylacrylate) is shown in Figure 4.3.
However, in the case of block copolymers such as polyurethanes, such a macrophase separation does not usually occur since the chemically incompatible sequences are confined by their covalent connections as illustrated in Figure 4.1. The result is that phase separation is on a much finer scale and interphase adhesion is complete. Structures that form from block copolymers still reflect phase incompatibility but at the same time are highly influenced by the forced intimacy of the phases . This can result in a new menu of structures such as the one shown in Figure 4.4.
Figure 4.3 Scanning electron micrograph of a 20/80% (w/w) blend of crosslinked polydimethyl siloxane in polymethyl methacrylate showing macrophase separation and minimization of interfacial surface area. Full scale = 100 |jm. Reprinted with permission from Ref. . © Elsevier Pub.
Figure 4.4 Tapping mode atomic force microscopy (AFM) of a TPU comprised of 40% hard 4,4' methylene diphenyldiisocyanate hydroquinone dietherethanol (MDI-HQEE) and polycaprolactone. Structure shows a cylindrical structure with no obvious orientational ordering. Full scale = 500 nm.
The incompatibility is reflected in the Flory interaction parameter (conventionally denoted by the Greek letter x (chi)):
In Equation 4.1 vref is a reference volume that can represent a monomer unit such as that for PO (58 cm3/mol) while 8 is a solubility parameter (sometimes called the Hildebrand solubility parameter or the van Krevelen solubility parameter) The solubility parameter is a measure of a material's ability to interact with another. Two materials with similar solubility parameter will be able to interact or mix, while those with different solubility parameters will phase separate. 8 is calculated from the cohesive energy density that is a measure of the energy needed to remove a unit of molecules from the molecules surrounding them. Equation 4.1 can then be rewritten as
Cohesive energy densities can be simply calculated using group additivity relationships provided in several well-known references [12, 13]. Polymer phase separation is strongly driven by the repulsion of unlike sequences even when the solubility parameters of the monomers of each sequence are relatively close. This is a result of
the very unfavorable enthalpy of mixing different polymer phases resulting in the driving force of polymer or block phase separation being driven by xN where N is the number of repeat units in the polymer chain or in the block sequence. Despite the block repulsion which in the case of polyurethanes can begin at quite low N values [3, 14], the effect of the forced intimacy of the blocks resulting from their covalent attachments is to potentially produce periodic structure such as shown in Figure 4.4. The structures that form will be a result of the block incompatability, the volume fraction of the blocks, and often processing conditions which can greatly complicate a priori quantitative prediction of final structure . When homopolymers phase separate, they are usually observed to minimize their interfacial surface area as seen in Figure 4.3. When block copolymers phase separate, they may form spherical structures, but they may also form alternative structures such as elongated cylinders shown in Figure 4.4, spherical structures such as observed in Figure 5.6b, or lamellar structures as shown in Figures 5.6a and 4.5. In limited cases, a gyroid structure such as Figure 5.9 may be observed (Table 4.1).
Figures 4.4 and 4.5 point out the very important role that the relative phase volumes play in the final phase-separated polyurethane structure.
Theoretical treatments of microphase separation transitions such as illustrated by Figures 4.4 and 4.5 result in phase diagrams typified by Figure 4.6. The boundaries indicate the combined effects of incompatibility and molecular weight (i.e., xN) on phase separation and structures. The equation by which the phase boundaries are computed is as follows.
Figure 4.5 Polyurethane elastomer of the same composition as the polyurethane in Figure 4.4 except having 45% hard segment. Full scale is 1 |om.
TABLE 4.1 Examples of solubility parameters calculated by the method of Bicerano
To convert to Pa1/2 multiply by 2.045. aRef. .
Figure 4.6 Illustrative phase diagram of a polyurethane capable of exhibiting different phase structures as a function of hard segment volume or molecular weight.
The details of this equation are reasonably straightforward but mask a very sophisticated derivation and line of reasoning . The value (xN)o is the value of xN below which there will be no phase separation. In Figure 4.6, it is approximately 18. This value is particular for polyurethanes and is the limit below which all phase boundaries converge to a disordered phase. The value of 10.495 has been calculated for xN representing infinite molecular weight diblock copolymers. The effect of the finite and poly-disperse molecular weight of polyurethanes and their multiblock structure is to increase XNo [6, 7]. This is equivalent to a suggestion that for multiblock and polydisperse block, and crosslinked copolymers such as a polyurethane, a higher level of phase incompatibility is required to obtain structured phases. Alternatively, it could be interpreted that for a block copolymer such as a polyurethane, a disordered phase can be obtained upon heating to a lower temperature than an ideal diblock of infinite molecular weight. In other words, one must cool from a melt to a lower temperature to obtain microphase separation. The constant 0.25 is calculated from the expression f(1 —f) for the value above which one would expect a phase inversion. In the illustrative case depicted in Figure 4.6, phase inversion occurs at a hard segment fraction f) greater than 0.5. It can also be intuitively thought of as the ratio of the two blocks in any single chain. The term ai represents the evaluation (calculated, measured, or guessed) for f(1 —f) resulting in a phase boundary for a particular morphology i. Thus in Figure 4.6, the phase boundary for the disordered/spherical transition is calculated with ai=0, for the spherical to cylindrical phase transition ai=0.098 and for the cylindrical to lamellar transition ai=0.206. Conditions in which multiple phases can be simultaneously observed have been treated as a special case for the common occurrence where mixing of reactants is nonideal or the hard segment fractions are very close to the phase boundaries and statistical fluctuations may result in phase diversity. The means by which these phases form from the melt and affect properties is discussed in the following.
The phase separation mechanism by which phase morphologies (Fig. 4.6) can occur has been reviewed and has been validated experimentally for polyurethanes [16-19]. Since polyurethane is simultaneously forming, phase separating, and potentially creating a gaseous coproduct, the path from high temperature melt to final product is quite a bit more complicated than that for an ideal block copolymer. For example, considerations of ideal block copolymers are that as the melt cools (quenches), the overall system free energy is at a minimum at each temperature arriving at a final equilibrium structure at the final state. The depth of quench is sometime referred to as the difference between the upper critical solution temperature and the system temperature . In reactive systems like polyurethanes, the system is evolving both chemically and rheologically, changing the definition of equilibrium conditions continuously (i.e., there is no reference state). Furthermore, as the reactions proceed and oligomers of hard segment coupled to soft segment form, they can act as surfactants with the resulting change in the distribution of x values and the interfacial energy of components in the mixture. In this case, the quench is potentially determined by temperature and simultaneously by the degree of conversion to polymer. As the polymer is forming and the block repulsions are initiating phase separation, the phases may separate by either nucleation and growth or by spinodal decomposition.
The difference between nucleation and growth and spinodal phase separation mechanisms is critical to understanding final polymer morphologies and controlling properties via formulation and processing [18, 19]. In a phase separation by nucleation and growth, the sample is quenched to a state where the solubility of each pure phase of the block exceeds the capacity of the melt. The phase separation begins as the homogeneous mixture enters this unstable region of the phase diagram (Fig. 4.7). Nucleation and growth is the expected mechanism when the system temperature proceeds slowly to the binodal curve . The composition of the phase-separated region proceeds along the arms of the binodal (or coexistence) curves to a composition
Figure 4.7 The case for polyurethanes is decomposition through the upper critical solution temperature upon temperature decrease or molecular weight increase.
of two major phases, each one solubilizing the minor component at the solubility limit of the other phase . Nucleation occurs since in this mechanism dispersed nuclei of each phase will form in the melt as the activation energy for nuclei formation exceeds the free energy of surface formation [23, 24]. Radiation scattering such as small angle x-ray scattering (Section 184.108.40.206) from a system phase separating by a nucleation and growth mechanism will exhibit a linear decrease with scattering angle and increase with time at a fixed angle according to Equation 4.4.
Time lag prior to the inception of nucleation, t, is often arbitrarily made zero. The value n for nucleation and growth is well established to be between 3 and 4 such that a plot of log intensity increase with log time at a fixed angle will have a slope between 3 and 4. This behavior is strong evidence for a nucleation and growth mechanism of phase separation.
In the case of spinodal phase decomposition, the system is rapidly quenched (i.e., cooled rapidly or made unstable by rapid molecular weight growth) and the system will occupy an unstable position bounded by the spinodal curve of Figure 4.7. In this case, phase separation will initiate through the existing concentration fluctuations with increasing amplitude and with a characteristic interphase spacing. The separating phases will form two co-continuous and sometimes inter-penetrating structures [20, 25-27]. In some cases, the final morphology may assume the appearance of a structure developed by nucleation and growth due to phase coalescence and coarsening at long times. However, the difference in mechanism as measured by radiation scattering is diagnostic. In a spinodal decomposition, the system may exhibit a time lag in the development of structure; however, once phase separation begins, intensity will grow at a characteristic angle which can be translated via the Bragg equation (5.6) into a characteristic spacing. The scattering intensity will have a finite breadth reflecting inhomogeneity of the periodicity within the sampled volume, but the maximum will be at constant angle and will exhibit exponential growth according to Equation 4.5 where R(q) is the amplitude growth rate of fluctuations of wave number q.
Thus a plot of ln I(q,t) versus time (t) should yield a straight line during the early stages of phase separation. While there is no question that the reaction-induced phase separation that occurs during polyurethane polymerization is different from the thermally induced phase separation upon cooling the melt of an ideal block copolymer, the behavior of polyurethane foam during foam formation exhibits scattering behavior consistent with a spinodal mechanism for phase separation. In the case of thermoplastic elastomers, the resulting structure can be consistent with either mechanism of phase separation. Specific elastomer processes can certainly exhibit the appearance of a phase separation that has developed via nucleation and growth (Fig. 4.8) using a slow cooling process, and also scattering signatures not confirming
Figure 4.8 TEM of a cast polyurethane elastomer with 35% 4,4' methylene diphenyldi-isocyanate 1,4 butanediol (MDI-BDO) hard segment with spherulitic appearance typical of a nucleation and growth phase separation. Polymer was formed at 85°C and sat quiescently at temperature for 4 h.
spinodal decomposition using a fast reactive injection molding process . Many other thermoplastic polyurethanes (TPU) elastomers will exhibit finely divided co-continuous gross morphologies typical of spinodal decomposition .
The significant differences in appearance observed between a morphology from spinodal and nucleation and growth mechanisms are a result of the difference in details of the mechanism. In both mechanisms, the individual blocks of an A-B block copolymer will possess some level of mutual insolubility and solubility in the melt. As the blocks diffuse, the local concentrations of components will exhibit increasing fluctuations. Fick's law stipulates that flux of an ideal mixture will be proportional to a concentration gradient.
For nonideal mixtures or solutions, the driving force is the gradient of chemical potential.
In Equations 4.6 and 4.7, D is the diffusion coefficient proportional to the squared velocity of the diffusing particles depending on temperature, viscosity of the surrounding medium, and the size and shape of the diffusing block, and C is the concentration of the individual species.
If the value of 3|iAB/3CAB is positive, then the diffusion coefficient is positive and diffusion occurs in the direction from high concentration to lower concentration as usually observed. When 3|iAB/3CAB is negative, then the direction of diffusion is from lower concentration to higher concentration. The former case is typical of diffusion occurring in a nucleation and growth mechanism [28, 29]. This is because the interface between two phases growing along the binodal curve is "infinitely" sharp and so the concentration just outside this phase is quite low, and away from the growing separating phase, the concentration of species is relatively higher. The latter case is typical of phase growth by a spinodal mechanism. This is because the phase formed via spinodal separation is not sharp and the concentration between concentration fluctuation waves is relatively lower between the concentration wave peaks yet still diffuses in the direction of the higher concentration peaks. In some cases and at long times, the morphology created by a spi-nodal decomposition and nucleation and growth mechanism can be indistinguishable due to coarsening ("Ostwald ripening") of the spinodal phase structure with time.