A review on microphase separation measurement techniques for polyurethanes

Abstract

Polyurethanes (PUs) microstructure and characteristics is strongly affected by microphase separation that arises from the thermodynamic immiscibility between the hard and soft segments. The extent of phase separation as well as the morphology and size of the separated phase governs their mechanical, electrical, thermal, and functional properties. This review: (1) provides an insight into how phase separation affects PU properties, (2) explains methods used to study PU phase separation. We review approaches from the simplest one, that is, the transparency measurement, to the more advanced methods including the spectroscopic techniques (infrared, nuclear magnetic resonance spectroscopies and X-ray scattering), rheological instruments (rheometrics mechanical spectrometer), and thermal analyses (differential scanning calorimetry). We also discuss the theoretical calculations and the molecular modeling used to study PU phase separation.

Keywords

polyurethanes phase separation microstructure hard segment soft segment

Introduction

Polyurethanes are block copolymers with a well-known microphase separation.^1,2 The microphase separation originates from the thermodynamic immiscibility between the hard and soft PU segments.^3–5 How much phase separation as well as the morphology and size of the separated domains strongly affects the mechanical, thermal, electrical, and functional properties. Controlling the phase separation can strongly influence PU properties.⁶ Molecular weight and polarity of the polyol,^7–9 chemistry and structure of the isocyanate and chain extender,^10–14 isocyanate, polyol and chain extender ratios,^15–17 utilization of additives in polymerization process,¹⁸ functionalization of the polymer chains^19–22 and application of shear field and the thermal process^23–25 can potentially affect the phase separation and accordingly the PU properties.

Increased phase separation usually augments the PU mechanical properties including the ultimate strength, modulus, and elongation at break. In this regard, increased hard segment content,^26–29 using aromatic and symmetric isocyanates^30–33 and including nanofillers like carbon nanotubes (CNTs)^34–36 increase the phase separation and positively influence the PU mechanical properties. It has to be noted that the positive relation between phase separation and mechanical properties is not ubiquitous. The polyether polyols impose more phase separation comparing the polyester counterparts. However, the tensile strength and modulus of the polyester polyurethanes are higher than those of the polyether counterparts. Indeed, the higher intermolecular interaction surpasses the higher phase separation.

The PU thermal properties also show a strong dependence to the microphase separation. Increased microphase separation forms hard segment and soft segment rich phases. Increased hard/soft phase purity substantially affects the temperature and strength of thermal transitions including glass transition, melting and crystallization.^37,38

In comparison with above mentioned properties, how phase separation affects the PU nanocomposite electrical properties has not been investigated extensively. This negligence is due to the small effect of phase separation compared to the filler properties on the electrical conductivity. Nevertheless, if the phase separation makes the conductive particles become more isolated, the electrical conductivity decreases and the percolation threshold increases.

A strong relation between phase separation and shape memory of the PUs has been already outlined.^39–41 Adjusting the phase separation to an optimum value can improve the PU shape memory parameters including the shape retention and shape recovery.

Since the microphase separation process can influentially affect the PU final properties, studying phase separation process and the different approaches for measuring the degree of phase separation are of the utmost importance.

So far, the phase separation has been studied by many techniques both qualitatively and quantitatively. Spectroscopy based techniques including Fourier transform infrared (FTIR)^25,42 and nuclear magnetic resonance (NMR) spectroscopy,^2,43 rheological analyses including temperature sweep and time sweep,^9,44 thermal analyses like differential scanning calorimetry (DSC),^45,46 crystallography approach like small-angle X-ray scattering (SAXS),^47,48 simulation studies like molecular dynamics (MD) simulation^49–51 and theoretical calculations can be used to study the PU microphase separation.

FTIR with quantitatively evaluating the hydrogen bonded N-H or C=O moieties vibrations and normalizing to the free moieties calculates the degree of phase separation. HNMR and CNMR spectroscopy study the N-H chemical shifts and C=O functionalities. Both provide qualitative information on hydrogen bonding between hard-hard as well as hard-soft segments. Spin diffusion solid-state NMR can quantitatively assess the PU phase separation and shed light on the phase separation degree, hard domain size, and hard/soft interphase thickness. Rheometrics mechanical spectrometer (RMS) enables studying the PU phase separation both qualitatively and quantitatively. Temperature sweep analysis measures the phase separation temperature, whereas time sweep analysis provides the phase separation kinetics and extent. DSC calculates the degree of phase separation based on the heat capacity changes at glass transition temperature (T_g). Moreover, the weight fraction and T_g of the soft segment rich phase can be obtained by DSC. SAXS is a structural analysis which measures the degree of phase separation based on the electron density variances.

With respect to theoretical approaches, calculating the PU interaction parameter and normalizing to the critical interaction parameter renders the degree of phase separation. Moreover, the comparing the soft and hard segment solubility parameter provides an insight into probability of the phase separation.

MD simulation is an interesting and innovative approach to study PU phase separation.^51–54 MD can study the PU phase separation directly by estimating the PU interaction parameter as well as the hard and soft segments solubility parameters.

In this review, we aim to describe how phase separation influences PU properties and to explain the different methods for studying PU phase separation details.

Phase separation of polyurethanes

The reaction between di or tri-isocyanates and polyols in the presence of hydroxyl or amine terminated chain extenders results in polymer chains with urethane linkages which are known as polyurethanes.^55,56 PUs are block copolymers with hard and soft segments.⁵⁷ The soft segments are polyol chains, and the hard segments are isocyanates and chain extenders^58–60 (Figure 1).

The PU microphase separation originates from the immiscibility between the hard and soft segments.⁶¹ The hard and soft segments have different physical and chemical properties. From the physical point of view, the soft segments are mainly in coil conformation. They possess a low Flory characteristic ratio and hence high flexibility and mobility. Whereas the hard segments have a high Flory characteristic ratio and are very stiff and immobile. From the chemical viewpoint, the soft segments have low polarity and melting point, while the hard segments are highly polar and melt at higher temperature. The physical and chemical immiscibility between hard and soft segments result in formatting micro domains which while compatible in macroscale are incompatible in microscale. The phase separated domains may possess globular, fibrillary or lamellar structure which dictate the PU final properties.⁶²

Due to phase separation, the soft segments form the matrix and the semi-crystalline or amorphous hard segments are dispersed into soft segment matrix.⁶³ The soft segments provide elastomeric features, whereas, the hard segments act as reinforcing components and provide dimensional stability.^64,65

Hydrogen bonds between the hard segments is the main cause of microphase separation. Hydrogen bonding in PUs occurs between urethane-urethane, urethane-ether, and urethane-ester functionalities. These hydrogen bonds have different energies such as 23.6 kJ/mol for urethane-ether, 25.6 kJ/mol for urethane-ester and 46.5 kJ/mol for the urethane-urethane bond. The strong hydrogen bonding between urethane-urethane groups leads to the phase separation, whereas the fairly weak hydrogen bonding between urethane-ether and urethane-ester functionalities gives rise to phase mixing.⁶⁶

Flory-Huggins interaction parameter (equation (1)) can predict the possibility of phase separation in PUs^51,67

χ_{A B} = \frac{Z [\frac{ε_{A B} - (ε_{A A} + ε_{B B})}{2}]}{K_{B} T}

(1)

where

Z	=	lattice coordination number
$ε_{A B}$	=	AB interaction energy
$ε_{A A}$	=	A-A interaction energy
$ε_{B B}$	=	B-B interaction energy
K_B	=	Boltzmann constant
T	=	absolute temperature.

Generally, a positive $χ$ value represents repulsion between phases and thus phase separation, whereas a negative $χ$ value suggests phase attraction and thus phase mixing.⁶⁸

The Flory-Huggins parameter ( $χ$ ) can predict the extent of phase separation in PUs. In PUs, the phase separation driving forces compete with entropic forces and not only determine the possibility, but also dictates the how much the phases separate.

For $χ N$ (N is degree of polymerization) less than 10.5, the entropic forces will dominate, and phase mixing happens, whereas for greater $χ N$ , phase separation driving forces will dominate and phase separation occurs. The higher the $χ N$ , the higher the phase separation will be.⁶⁹

Significance of polyurethanes phase separation

The occurrence of microphase separation and formation of microphase separated domains can give excellent properties to PUs. The microphase separated hard domains are like physical crosslinking and make polyurethanes perform like a crosslinked network. Compared to chemical crosslinking, physical crosslinking due to phase separation is reversible. Once the temperature increases, the hydrogen bonds between hard segments become weaker and phase mixing becomes prominent. Therefore, PUs unlike chemically crosslinked polymers can be melted and recycled. As the phases separate physical crosslinking occurs and the PU mechanical properties including stiffness and flexibility improve. Therefore, with phase separation control, it is possible to change PU mechanical properties and develop PUs for different applications going from flexible and soft foam, soft plastic, flexible elastomer to hard foam, hard solid plastics, and also thermoplastic elastomers.⁴⁷

Another significant aspect of PU phase separation is shape memory capability. Shape memory for PUs is a function of the phase separation between hard and soft segments. Unlike metal alloys in which shape memory occurs due to martensitic/austenitic phase transition, PU shape memory occurs due to polymer chain conformational changes in soft segment rich phases.⁷⁰ The shape memory is a very interesting property and enables special PU applications such as vascular stent, thrombus filter, self-repairing automobile and aircraft parts, and window sealant.

Effect of nanoparticles on polyurethanes phase separation

Nanoparticles such as carbon nanotubes (CNTs), carbon fibers (CFs), halloysite nanotubes (HNTs), and carbon black nanoparticles (CBNPs) can be added into a PU matrix to modify its mechanical, electrical, thermal, and barrier properties.^71–73 The nanoparticles substantially affect the PU phase separation (Figure 2). The nanoparticles usually increase the extent of phase separation due to the fact that they provide a platform for hard segment accumulation.³⁷ For instance, Farzaneh et al.³⁷ have corroborated that with increasing CNT content from 0% to 0.4%, the phase separation degree increased by 25%. However, the nanoparticles with the diameter smaller than the polymer gyration radius can decrease the phase separation. Because these nanoparticles act like a compatibilizer and increase the miscibility of the soft and hard segments. The effect of nanoparticles on PU phase separation is governed by the particle size, aspect ratio, shape, chemical nature, surface charge as well as the particle arrangement and interaction with polymer chains. It has to be noted that different nanoparticles have different propensities toward hard and soft segments, for instance CNTs have high tendency to hard segments, whereas CBNPs possess high affinity to the soft segments. Therefore, they discriminately modulate the properties of hard segment and soft segment rich phases.^74,75

Effect of phase separation on polyurethane properties

How much the phases separate as well as the morphology and the separated domain size strongly affects the PU properties. As mentioned before, the microphase separation enables special properties to PUs. Therefore, controlling microphase separation is a possible approach for modulating PU properties. Mechanical, electrical, and functional behaviors can be affected by microphase segregation. First and foremost, the microphase separation highly affects their mechanical properties. The microphase separation can be influenced by many parameters including material related as well as process related parameters. Material related parameters can refer to polyol polarity and molecular weight, isocyanate chemistry and structure, chain extender type and different nanoparticles. The process related parameters allude to the shear field applied and thermal annealing during or following PU synthesis (Figures 3 and 4).

Phase separation and mechanical properties of polyurethanes

Molecular interactions between soft and hard segments prohibit the plastic flow under loading and provide the outstanding mechanical behavior to PUs. Once the mechanical stress is applied to PU, the hard segments moderately become aligned along the applied stress and several hydrogen bonds are formed between the adjacent hard segments which tremendously increases the tensile strength and elongation.

In general, increased phase separation and hard domain formation boosts tensile strength, tensile modulus and elongation.⁷⁶ Indeed, the separated hard domains act as crosslinking between soft domains.^77,78 However, very high phase separation may result in high brittleness and low extensibility.

It has to be noted that hydrogen bonding is a main driving force for microphase separation and the hydrogen bond strength dictates the mechanical properties. The hydrogen bonding can occur between both hard-hard and hard-soft segments. Hard to hard bonding leads to phase separation, whereas hard to soft bonding leads to phase mixing. It has been proved that high phase separation results in the superior (high strength, high modulus and elongation at break), whereas high phase mixing results in lower mechanical properties.⁷⁹

One important parameter affecting the degree of phase separation and the mechanical properties is the hard segment percentage (Figure 5). With increased percent hard segments, the tensile strength and modulus increase which can be assigned to the higher hydrogen bond formation between hard segments and creating more hard domains. However, there is an optimum hard segment percent in which the highest phase separation, modulus, and strength are achieved. Amrollahi el al.⁷⁸ have corroborated that between 48 - 52% hard segment gave the maximum degree of phase separation (DPS) and hydrogen bonding index (HI). The higher hard segment content would confine polymer chain mobility and confer numerous hydrogen bonds to PUs which causes PU rigidity and its failure at lower elongation.

Another influential parameter controlling PU mechanical properties is the isocyanate to the hydroxyl groups (NCO/OH) molar ratio or isocyanate index.⁸⁰ This ratio can be tuned PU components type such as isocyanates, polyols, and chain extenders along with their concentration. The control over this ratio strongly affects the microphase separation.⁸¹ It has been reported that equimolar ratio of these groups can result in the minimum phase separation. Pukánszky et al.⁸² have corroborated that with increasing NCO/OH ratio from 0.9 to 1, phase separation decreases 10 fold. The NCO ratio less than or greater than 1increases the phase separation and decreases the soft segment number and flexibility, both of which increase polymer stiffness. For lower NCO content, the short chains with hydroxyl end groups are formed and the strong hydrogen bonding between these groups facilitates the microphase separation. Whereas, for higher NCO content, the amine end groups augment the phase separation.

How the phase separation affects the tensile strength and elongation was not similar to the effect on modulus. That is because more parameters come into play which dictate the ultimate strength and strain. With increasing NCO to OH ratio, the polymer chain lengths increase and chain entanglement is promoted which in turn increases the ultimate strength and elongation.⁸²

In addition to isocyanate content, the isocyanate structure affects the PU mechanical properties. The aromatic isocyanate based PUs are better than the aliphatic ones with respect to mechanical strength and modulus. However, PUs with aromatic isocyanates gradually yellow due to forming a quinoid structure.

Isocyanate symmetry or asymmetry also is an influential parameter on mechanical properties. Using the symmetric isocyanates including trans-1,4-bis(isocyanatomethyl)cyclohexane (1,4-H6XDI) enhances the cohesion between hard segments and increases the degree of phase separation which in turn increases the tensile modulus and elongation at break. Nozaki et al.³³ have corroborated that the tensile modulus, tensile strength, and elongation at break increased by 137%, 16%, and 50% in 1,4-H6XDI based polyurethane versus the MDI based one.

The hard domains can perform as filler or crosslink in PU matrix. The filler domains impart high modulus, whereas the crosslink domains provide high elongation. With the increase of applied strain, the hard domains transform from filler to crosslink and the extent of this transformation is influenced by the chemical compositions of the feeding stocks especially the type of the isocyanates.

Stribecka et al.⁴⁷ studied how three isocyanates, that is, methylene diphenyl diisocyanate (MDI), hydrogenated, isomeric MDI (H₁₂MDI) and hexamethylene diisocyanate (HDI) affected the filler-crosslink domain conversion and the mechanical properties. The results corroborated that aliphatic isocyanate (HDI) based PU has the highest possibility for the filler-crosslink domain conversion and the lowest modulus. Whereas the H₁₂MDI based counterpart had the lowest possibility for the filler-crosslink domain conversion and the highest modulus. The filler-crosslink domain conversion occurs when the adjacent hard domains touch one another. Strain induced crystallization of hard domains decreases the distance between the hard segment rich phases. In aliphatic isocyanates, the hard domain crystallization is more possible. The higher the crystallization in the hard domains, the more easily the hard domains can touch each other and the filler to crosslink domain conversion is more likely.

How the phase separation influences the mechanical properties is strong insofar as adding low nanoparticle concentrations can substantially affect the phase segregation in the nanocomposite and change the mechanical response versus the neat polymer. The disruption or promotion of phase separation and the depression or amplification of mechanical properties rely on the nature and the extent of interactions between the polymer chains and nanoparticles. PU phase segregation follows a two-stage process; in the first stage, the hard segments assemble and the hard segment rich 10 nm domains form. In the second stage, the 10 nm hard segment rich phases associate with one another and 40–100 nm hard domains develop. It has been reported that nanoparticles such as zinc oxide (ZnO) and aluminum oxide (Al₂O₃) impede the second stage of PU phase separation and decrease the degree of phase separation and accordingly the elastic modulus and elongation.⁸³ On the other hand, CNTs improve the PU nanocomposite phase segregation and increases the elastic modulus and tensile strength.^71,84

Phase separation and thermal properties of polyurethanes

The extent of phase separation strongly affects the PU thermal properties including glass transition, melting and crystallization behavior. Increased phase separation creates higher purity hard and soft segment rich phases which in turn determines their thermal behaviors.

For a typical PU dynamic mechanical analysis (DMA) spectrum, two main transitions can be observed; the one between −100 to −70°C and the other between 55 to 110°C.^74,85–87 The first transition can be assigned to the soft segment rich phase glass transition and the second can be ascribed to the hard segment rich phase glass transition. In general, with increased phase separation, the soft segment T_g decreases. Because the hard segments which are mixed with the soft segments are extracted and the soft segment rich phase purity is greater than before. Therefore, the soft segments have more freedom to move. The higher segment mobility decreases the T_g, whereas their higher number increases the glass transition intensity.⁸⁸ Indeed, the increased T_g for the soft segment rich phase suggests a higher phase miscibility.

In PU nanocomposites, more parameters affect PU glass transition behavior. Although, the filler mostly increases the phase separation and increases the soft segment purity. However, the filler particles, for instance carbon fibers, are usually larger than the polymer chains and confines the chain mobility and segmental motions which accordingly raises the soft segment T_g. Phase separation influences the hard segment T_g too. The higher the phase separation, the higher the hard segment T_g will be.

With respect to the melting, increased phase separation and as a result increased hard segment rich phase, the melting temperature and enthalpy increases. It is noted that sometime a double melting peak for the hard segment rich phase is observed in DSC thermogram which can be assigned to two crystalline morphologies. The one in the mixed phase and the other in hard segment rich phase. Increased phase separation increases the double melting phenomenon.

Concerning the crystallization, the higher the phase separation, the sooner the crystallization occurs. Because the samples with more thermodynamic immiscibility have more tendency to crystalize. Moreover, the decreased hard and soft segment mixing allows for soft segment organization into the crystalline structures. The higher phase separation facilitates the pure soft domain formation and soft segment crystallization.

Phase separation and electrical properties of polyurethanes

The phase separation extent and their sizes potentially affects the PU nanocomposite electrical behavior. However, this subject has not been extensively addressed. Because the change in particle type and content induces a substantial effect on electrical conductivity and increases or decreases the conductivity by several order of magnitudes, whereas the change of phase separation extent and morphology imposes a subtle influence on PU nanocomposite electrical behavior.

The electrical conductivity and the percolation threshold are dictated by the conductive nanoparticle’s nature, the nanoparticle arrangement in the matrix and the PU properties. In nanocomposites, the electron transport between conductive particles occurs via a tunneling mechanism in which the electrons jump through the intervening polymer layer. Therefore, the polymer layer properties surrounding the particles inevitably affect the composite electrical properties.^89–91

How the phase separation affects the PU nanocomposite electrical conductivity relies highly on the nanoparticle affinity to the hard or soft segments. As phase separation increases and more hard segment rich domains form in PU/CNT nanocomposites the electrical conductivity can decrease. Because CNTs have high affinity to the hard segments and offer a platform for hard segment aggregation the phase separated hard domains cover the CNTs and impede electron mobility.

Phase separation and shape memory of polyurethanes

PU shape memory properties originate from the phase separation.⁹² Because phase separation results in forming the hard segment and soft segment rich phases. The hard segment rich phase acts as a stationary or permeant phase and preserves overall polymer structure during loading.⁹³ Whereas, the soft segment rich phase performs as a mobile or reversible component and confers shape memory to PUs.⁹⁴ Thermo-responsive shape memory of PUs occurs at temperatures where the soft segments can move (either T_g or T_m). With the increase of temperature to this point, the segments become soft and free enough to restore the unstretched conformation.⁷⁰ The heating is not the only stimulus for PU shape memory. Other stimuli including electrical current and magnetic field can make the PU recover its original state if electrically conductive fillers are included into the PU matrix.⁹⁵ Controlling the soft segment molecular weight, hard to soft segment molar ratio, the polymerization process and the process parameters can tune the microphase segregation and the shape memory.⁹⁶ The higher the phase separation, the better the shape memory.

Similar to how the hard segment affects the mechanical properties, the hard segment content powerfully influences the PU shape memory. The literature reports that when the hard segment content increases from 30 to 50%, the shape memory parameters, that is, shape retention and shape recovery, improve. Indeed, in this hard segment content range, enough hydrogen bonds form between the hard segments which enables the structure and shape to recover. With more hard segments, the structure becomes more rigid and the shape memory is not measurable anymore. Moreover, with the hard segment content below 30%, shape memory is not detected.⁹⁶

The hard segment structure profoundly affects the phase separation and the functional properties. Wu et al.⁹⁷ have corroborated that branched hard segments augment the microphase separation and improve the shape memory properties giving rise to high shape retention and shape recovery. Branched hard segments impede hard segment crystallization and promote the soft segment crystallization. Both of which result in frozen soft segment rich domains linked to each other by hard segment rich domains crosslinking points. The increased microphase separation degree as well as the particular microphase structure of the resulting PU are the reasons for the improved shape memory properties.

The polyol and its molecular weight are influential parameters that determine PU shape memory. Trinh et al. corroborated that polyether polyols give rise to the superior shape memory properties comparing the polyester counterparts. Moreover, the shape memory improves in parallel with the increased polyol molecular weight.⁹⁸

Adding functional groups which make thermo-reversible molecular interactions can increase the interactions between hard segments and promote phase separation. The higher the phase separation, the higher the shape memory. Ha et al.⁹⁹ have introduced disulfide bonds into the main PU backbone PU using 2‐hydroxyethyl disulfide (HEDS) in composition. The analyses corroborated that the disulfide bearing functionalities improves the molecular interaction between hard segments and gives rise to a well-developed phase separated structure and thus augments the PU shape recovery (Figure 6). Healing efficiency increased by 103–360% at 50°C and by 200–216% at 70°C in PU with disulfide bonds versus the PUs without disulfide bonds.

It is possible to substantially affect the microphase separation and the resulting shape memory without changing the type and content of the hard and soft segment. The subtle variation in polymerization process and adding some additives can be a convenient approach for influencing the microphase separation. Chen et al.¹⁸ reported that when a low molecular weight lubricant, that is, 1-octadecanol (ODO) at 0.3–0.9%, was introduced to the polymerization mixture. ODO was added to the end of the PU chain via the interaction between PU urethane groups and ODO hydroxyl functionalities. The ODO presence increased the hard and soft phase immiscibility and hence the microphase separation. As a result, the shape memory parameters of the synthesized PUs including the recovery temperature, shape fixity and shape stability were improved.

PU not only can perform as a dual shape memory, but also as a multi-shape memory polymer. In the latter case, the PU can memorize more than one temporary shape. The multi-shape memory PUs can be synthesized by combining two or more polyols which results in a multi shape memory polymer with multiple switching temperatures.¹⁰⁰

Phase separation study in polyurethanes

PU phase separation studies follow many approaches both qualitatively and quantitatively. Transparency measurement, spectroscopy based techniques including FTIR and NMR, rheological analyses including temperature sweep and time sweep, thermal analyses like DSC, crystallography approach like SAXS, simulation studies like MD simulation and theoretical calculations can help study PU microphase separation. The details are discussed below.

Transparency measurement

Measuring transparency is a simple way to evaluate phase separation. Phase separation decreases optical transmission and is proportional to the degree of phase separation and the separated domains size. For this purpose, the transmission is measured at wavelength = 500 nm using a UV-visible spectrophotometer.⁸²

Fourier-transform infrared spectroscopy (FTIR)

FTIR is a simple and widely accepted methods to measure PU phase separation. The hydrogen bonding between hard segments strongly correlates with PU microphase separation. Therefore, in this method, the vibrations arise from the hydrogen bonded N-H or C=O moieties of the urethane group as well as those of free N-H or C=O moieties are considered and the degree of phase separation is calculated by the equations (2) and (3)^101,102

D P S = \frac{N - H_{h y d r o g e n b o n d e d}}{N - H_{h y d r o g e n b o n d e d} + N - H_{f r e e}}

(2)

D P S = \frac{C = O_{h y d r o g e n b o n d e d}}{C = O_{h y d r o g e n b o n d e d} + C = O_{f r e e}}

(3)

where

DPS	=	Degree of Phase Separation
$N - H_{h y d r o g e n b o n d e d}$	=	characteristic intensity absorbance at 3348 cm⁻¹
$N - H_{f r e e}$	=	characteristic intensity absorbance at 3445 cm⁻¹
$C = O_{h y d r o g e n b o n d e d}$	=	characteristic intensity absorbance at 1730 cm⁻¹
$C = O_{f r e e}$	=	characteristic intensity absorbance at 1703 cm⁻¹.

The hydrogen bonded N-H (C=O) stretching arises from the aligned urethane connections in the hard domains, whereas the free N-H (C=O) stretching originates from the mixed hard and soft segments. The higher the phase separation, the higher the hydrogen bonded N-H (C=O) stretching intensity will be.^101,102

Hydrogen bonding index (HI) is another criterion which can be calculated based on the FTIR spectra and is considered as a powerful criterion for measuring phase segregation (equation (4)). Higher HI represents higher phase segregation⁷⁸

H I = \frac{C = O_{h y d r o g e n b o n d e d}}{C = O_{f r e e}}

(4)

Nuclear magnetic resonance spectroscopy (NMR)

FTIR cannot perfectly represent the real PU microphase separation. Because in this method, the N-H or C=O moieties of the urethane group in interphase may not form hydrogen bonds and thus are omitted from the phase separation estimation. Moreover, it is noted that all carbonyl or amine functionalities in hard domains cannot make hydrogen bonds; therefore, they are neglected from the measurement.¹⁰³ Nuclear magnetic resonance spectroscopy (NMR) is a more precise approach to study phase separation in PUs.^104–106 NMR spectroscopy studies the chemical shift of the resonance frequency of the nuclear spin with applying an external magnetic field and a radio-frequency pulse thus providing the details of the atomic structure of the molecules. In ¹H NMR, the ¹H chemical shifts of NH group provide the information of hydrogen bonds between either soft-hard and hard-hard segments and thus the extent of phase separation. On the other hand, in ¹³C NMR, the ¹³C chemical shifts of C=O measure the hydrogen bonds between either soft-hard and hard-hard segments and thus the extent of phase separation.^107,108

NMR coupling with Magic Sandwich Echo (MSE) methodology enables one to study the soft, hard and interphase regions based on the discrete proton populations with different mobility. In this method, the proton populations with discrete mobility are a function of their relaxation time corresponding to PU different phases. The proton populations with low relaxation time are assigned to the hard phase and those with high relaxation time are assigned to the soft phase. And finally, the ones with intermediate relaxation time correspond to the interphase. The position and intensity of the discrete proton populations corroborate the relative contribution of hard and soft segment rich phases in PUs.¹⁰⁹

Spin diffusion is a spatial diffusion of nuclear magnetization from the first to the second phase, mediated by dipole-dipole interactions.¹¹⁰ Spin-diffusion solid-state NMR can be used to measure the degree of phase separation (

λ

), domain sizes (

d

) and soft/hard interphase thickness (

d_{i n}

). Degree of phase separation (

λ

) can be measured from ¹H dipolar filter spin diffusion NMR experiments using equation (5). The dipolar filter cancels the rigid phase magnetization and retains the mobile phase magnetization

λ = \frac{f_{m}}{f_{s m}}

(5)

where

$λ$	=	degree of phase separation
$f_{m}$	=	soft phase equilibrated proton ratio
$f_{s m}$	=	soft phase stoichiometric proton ratio.¹¹¹

For measuring f_m, ¹H spin diffusion curves with increasing filter strength (N_cycle) are plotted. The f_m is the proton ratio where the equilibrium value of the spin diffusion curve at different N_cycle remain unchanged.

The hard domain size can be calculated based on the spin diffusion theory using equation (6)⁴³

d = \frac{ρ_{A}^{H} φ_{A} + ρ_{B}^{H} φ_{B}}{φ_{A} φ_{B}} \times \frac{4 ε φ_{B}}{\sqrt{π}} \times \frac{\sqrt{D_{A} D_{B}}}{ρ_{A}^{H} \sqrt{D_{A}} + ρ_{B}^{H} \sqrt{D_{B}}} \times \sqrt{t_{m}^{s, 0}}

(6)

where

$φ_{A}$	=	Soft phase volume fraction
$φ_{B}$	=	hard phase volume fraction
$ρ_{A}^{H}$	=	soft phase proton density
$ρ_{B}^{H}$	=	hard phase proton density
$D_{A}$	=	soft phase spin-diffusion coefficients
$D_{B}$	=	hard phase spin-diffusion coefficients
$ε$	=	1 is representative of lamellar
$ε$	=	2 of cylindrical
$ε$	=	3 of spherical morphology
$t_{m}^{s, 0}$	=	characteristic mixing time of spin-diffusion

The mixing time is the duration in which the dipole-dipole interactions among the protons occur.¹¹²

For obtaining $t_{m}^{s, 0}$ , the normalized signal intensity (I/I₀) vales are plotted versus the square root of the mixing time and intercept of extrapolated initial linear-slope with the x-axis is considered as $t_{m}^{s, 0}$ .

D_B is given by equation (7)

D_{B} = \frac{1}{12} \sqrt{\frac{π}{2 \ln 2}} 〈 r^{2} 〉 Δ v_{\frac{1}{2}}^{B}

(7)

where

r ²	=	is the mean-square distance between the nearest spins which can be considered as 0.05 nm²
$Δ v_{1 / 2}^{B}$	=	is the full width at half height for proton signals of hard phase

D_A is provided by equations (8) and (9)¹¹³

D_{A} = 8.2 \times 10^{- 6} T_{2}^{- 1.5} + 0.007 0 < T_{2}^{- 1} < 1000 H z

(8)

D_{A} = 4.4 \times 10^{- 5} T_{2}^{- 1} + 0.26 1000 < T_{2}^{- 1} < 3500 H z

(9)

T_{2}

is nuclear spin transverse relaxation time which alludes to phenomenon of returning to the equilibrium magnetic state perpendicular to the applied magnetic field.

Moreover, the PU interphase thickness is expressed by the equation (10)

d_{i n} = (\sqrt[ε]{2 - λ} - \sqrt[ε]{λ}) \frac{d}{2}

(10)

where

$λ$	=	degree of phase separation
$ε$	=	dimensionality
$d$	=	hard domain size

Rheometrics Mechanical Spectrometer (RMS)

RMS is an outstanding approach for measuring not only the extent but also the temperature and time of phase separation process. To fulfill this, temperature sweep, time sweep and flow curve analyses should be conducted.

The cooling temperature sweep analysis determines the phase separation temperature,¹¹⁴ whereas the heating temperature sweep analysis measures the order-disorder transition temperature (T_ODT).¹¹⁵ During cooling from T_m to T_g, the temperature in which a sharp storage modulus increase occurs is designated as phase separation temperature. In heating regime, the temperature where a profound modulus decrease happens is considered as T_ODT. T_ODT arises from melting hard segments. Moreover, other transition temperature are detected from the heating regime. The one occurs in a lower temperature range and arises from hard domain movement and the other occurs in a higher temperature range and originates from the hard domain destruction. These transitions appear as smaller modulus drop before T_ODT.

In time sweep analysis, the storage and loss modulus cross time determines phase separation kinetics. Before the cross time, the PU is viscous, and the loss modulus is greater than the storage modulus. As time goes by, the storage modulus increases due to phase separation and forming a 3D network of hard segments.⁷³ The sooner the cross time occurs, the higher the phase separation speed. Avrami equation (11) can be used to provide a better insight into phase separation kinetics using time sweep curve (Figure 7)³⁸

G^{'} (t) = G_{0}^{'} + G_{\infty}^{'} {(1 - \exp (- k t^{n}))}^{2}

(11)

where

$G_{0}^{'}$	=	storage modulus at the beginning of time sweep analysis
$G_{\infty}^{'}$	=	storage modulus at the end of analysis
k	=	phase separation rate constant
n	=	Avrami exponent
$t_{1 / 2}$	=	descriptive of half-time of phase separation.

It is noted that in PU nanocomposites $t_{1 / 2}$ represents nanoparticle cluttering rather than phase separation.

The extent of phase separation can be calculated from the time sweep curve using the equation (12)⁴⁴

I G^{'} = \frac{G_{\infty}^{'} - G_{0}^{'}}{G_{0}^{'}}

(12)

Flow curve analysis studies the polymer response to the shear rate in a nonlinear region and determines how the PU structure separates under shear. The flow curve depicts viscosity or stress variations versus shear. Concurrent with the increased shear rate, the viscosity decreases and shear thinning behavior appears.¹¹⁶ The higher the phase separation, the higher the shear thinning. Whereas, the higher the phase mixing the lower the shear thinning. For a more precise study, power law model (equation (13)) can be used to calculate the exponent “n” describing the extent of shear thinning

(n - 1) = \frac{\log \frac{η_{2}}{η_{1}}}{\log \frac{\dot{γ_{2}}}{\dot{γ_{1}}}}

(13)

The exponent n varies from 0 to 1. The lower the n, higher the shear thinning.

Differential scanning calorimetry (DSC)

Quantitative differential scanning calorimetry is one of the best approaches to study PU phase separation. The degree of phase separation can be calculated from the increase of specific heat capacity at T_g using the equation proposed by Camberlin et al.¹¹⁷ with some modifications

α_{s e g} = [\frac{Δ C_{p, s s}}{Δ C_{p, o l i g} w_{s s}}] K_{s}

(14)

where

ΔC _p,ss	=	soft segment change in heat capacity at the glass transition
ΔC _p,olig	=	pure oligomer acting as soft segments in PU
w _ss	=	soft segment weight fraction
K _s	=	packing parameter and can be calculated from equation (15)

K_{s} = \frac{(N_{A} \sum V_{r})}{(\frac{M_{r}}{ρ})}

(15)

where

N _A	=	Avogadro number
V _r	=	repeating unit volume
M _r	=	repeating unit molecular weight
ρ	=	PU density.

In addition to degree of phase separation, the weight fraction of the soft segment rich phase can be calculated from the DSC thermograms using the equation (16)

F_{s s} = \frac{Δ C_{p}}{f_{s s} Δ C_{p, s s} + (1 - f_{s s}) Δ C_{p, h s}}

(16)

where ΔC_p and f_ss are given by equations (17) and (18)¹¹⁸

Δ C_{p} = w_{s s} Δ C_{p, s s} + w_{h s} Δ C_{p, h s}

(17)

f_{s s} = \frac{\frac{Δ C_{p, h s}}{Δ C_{p, s s}} (T_{g, h s} - T_{g})}{(T_{g} - T_{g, s s}) + \frac{Δ C_{p, h s}}{Δ C_{p, s s}} (T_{g, h s} - T_{g})}

(18)

where

ΔC _p	=	soft segment rich phase change in heat capacity at the glass transition
f _ss	=	soft segment rich phase weight fraction
ΔC _p,ss	=	soft segment heat capacity at the glass transition
ΔC _p,hs	=	hard segment heat capacity at the glass transition
w _ss	=	soft segment weight fraction
w _hs	=	hard segment weight fraction
T _g	=	soft segment rich phase glass transition temperature calculated by equation (19)

T_{g} = \frac{w_{s s} T_{g, s s} + \frac{Δ C_{p, h s}}{Δ C_{p, s s}} w_{h s} T_{g, h s}}{w_{s s} + \frac{Δ C_{p, h s}}{Δ C_{p, s s}} w_{h s}}

(19)

Small angle X-ray scattering (SAXS)

Quantitative evaluations of small angle X-ray scattering is a well-established method for measuring PU phase segregation.^119,120 The sample preparation for SAXS is very easy and PUs usually scatter strongly in the small angle region.¹²¹ In SAXS analysis, a monochromatic X-ray beam collides with the sample, interacts with electrons and is scattered. The scattering pattern provides the information on the sample structure. SAXS provides structural information between 1 to 100 nm. The PU scattering peaks arises from local heterogeneities in the electron density of the phase separated domains.^122,123 In SAXS spectra, the scattering intensity ( $I (q)$ ) is plotted versus the magnitude of the scattering vector ( $q = \frac{4 π S i n θ}{λ}$ , 2θ is scattering angle). SAXS can detect the phase separated domains from the mixed segments. A constant scattering background is obtained for the mixed segment, whereas a distinct scattering pattern above the background is observed for the phase separated domains in SAXS spectra.^124,125 Each curve has a scattering maximum, indicating the microphase separated structure.

SAXS is able to deliver information on the degree of microphase separation, inter-domain spacing and domain boundary diffuseness. The degree of phase separation can be estimated from SAXS data using the equation (20)^126,127

α = \frac{Δ η_{\exp}^{2}}{Δ η_{t h e}^{2}}

(20)

where

$Δ η_{t h e}^{2}$	=	theoretical electron density variance
$Δ η_{\exp}^{2}$	=	experimental electron density variance.

The theoretical electron density variance is given by equation (21)

Δ η_{t h e}^{2} = ϕ_{h s} ϕ_{s s} (η_{h s} - η_{s s})

(21)

where

$ϕ_{h s}$	=	hard segment volume fraction
$ϕ_{s s}$	=	soft segment volume fraction
$η_{h s}$	=	hard segment electron density
$η_{s s}$	=	soft segment electron density.

With the assumption of lamellar phase separated structure for PU and the implementation of Lorentz-corrected scattered intensity (

I (q) q^{2}

), the experimental electron density variance is provided by equation (22)¹²⁸

Δ η_{\exp}^{2} = c \int_{0}^{\infty} (I (q) - I_{b} (q)) q^{2} d q

(22)

where

$I (q)$	=	scattering intensity
$I_{b} (q)$	=	background intensity.

The SAXS spectra can be used to measure the inter-domain distances using Bragg’s equation. The peak position of maximum (q_max) indicates the mean inter-domain spacing

d = \frac{n λ}{2 π S i n θ}

(23)

With the consideration of

q = \frac{4 π S i n θ}{λ}

d = \frac{2 π}{q_{\max}}

(24)

q_{\max}

is q value at the maximum of I(q)q² plot versus q.

PU domain boundaries are more or less diffuse.

Δ η^{2}

measures the domain boundary diffuseness in PUs

Δ η^{2} = c \int_{0}^{\infty} \frac{(I (q) - I_{b} (q)) q^{2}}{H^{2} (q)} d q

(25)

where

H (q)

a function that relates to the interfacial boundary size and shape between the phases c = constant given by equation (26)

c = \frac{1}{2 π^{2} i_{e} N_{A}^{2}} = 1.76 \times 10^{- 24} \frac{m o l^{2}}{c m^{2}}

(26)

where

N _A	=	Avogadro’s number
i _e	=	Thompson’s constant for the scattering from one electron

Theoretical calculations

In addition to experimental analyses, theoretical calculations can be used to deduce the probability and the extent of PU phase segregation. To this aim, the PU interaction parameter is calculated (equation (27) and is compared with the critical interaction parameter (equation (31))^129,130

χ = \frac{ν_{r}}{R T} {(δ_{s s} - δ_{h s})}^{2}

(27)

where

χ	=	PU interaction parameter
$ν_{r}$	=	molar volume of TPU repeating unit
R	=	gas constant
T	=	Temperature
δ _ss	=	soft segment Hansen solubility parameter
δ _hs	=	hard segment Hansen solubility parameter
δ _ss	=	given by equation (28)
δ _hs	=	given by equation (29)

δ_{s s} = \sqrt{δ_{s s d}^{2} + δ_{s s h}^{2} + δ_{s s p}^{2}}

(28)

δ_{h s} = \sqrt{δ_{h d d}^{2} + δ_{h s h}^{2} + δ_{h d p}^{2}}

(29)

where

δ _d	=	Hansen parameter contribution from dispersion
δ _h	=	Hansen parameter contribution from hydrogen bonding
δ _p	=	Hansen parameter contribution from polar forces

and are provided by equation (30)

δ_{d} = \frac{\sum F_{d i}}{V}, δ_{h} = \sqrt{\frac{\sum E_{h i}}{V}}, δ_{p} = \frac{\sqrt{\sum F_{p i}^{2}}}{V}

(30)

where

F _di	=	dispersion ter
F _pi	=	hydrogen bonding term
E _hi	=	polar related term
V	=	molar volume

all of which are available in literature.¹³¹ The critical interaction parameter can be estimated using equation (31)

χ_{c r i t} = \frac{1}{2} {(\frac{1}{\sqrt{x_{s s}}} + \frac{1}{\sqrt{x_{h s}}})}^{2}

(31)

where

x _ss	=	number of soft segments
x _hs	=	number of hard segments

The ratio of the interaction parameter to critical interaction parameter dictates the extent of phase separation. The higher the $\frac{χ}{χ_{c r i t}}$ , the higher the phase segregation.

Molecular dynamics (MD) simulation

Molecular dynamics (MD) simulation has received increasing attention as a fascinating approach to study PU phase separation.^132,133 MD simulation analyses the physical movements of atoms and molecules in a complex system. The atoms and molecules are allowed to interact in a fixed interval, the dynamic evolution of the system occurs and an equilibrated state is achieved. The dynamically evolved or the equilibrated system can deliver valuable information of macromolecule behavior. This computer modeling is able to study the effect of the different parameters on the PU properties prior to the experimental research which profoundly decreases the cost and time needed for the extended experimental studies. With this simulation, it is possible to study PU physicochemical properties including the radius of gyration, fractional free volume, density, solubility parameter, persistence length as well as the PU transport properties including permeability and diffusion coefficient. For the MD simulation, the PU chains with the desired hard and soft segments moieties are included into the simulation cell and the analyses are performed on the equilibrated cell.

Radial distribution function (RDF) of MD corroborates the extent of interactions between hard segments as well as those between hard and soft segments. Indeed, g(r) describes molecular interactions between polymer chains. The position and intensity of the emerged peaks in RDF reveals the extent of interactions between the segments and thus the degree of phase separation or phase mixing (Figure 8)⁵¹

g_{A B} (r) = \frac{1}{ρ_{A B} 4 π r^{2}} \frac{\sum_{i = 1}^{K} \sum_{j = 1}^{N_{A B}} Δ N_{A B} (r \to r + δ_{r})}{N_{A B} \times K}

(32)

where

g(r)	=	represents the probability of finding a pair of atoms at a distance r with respect to the bulk phase in a completely random distribution
ρ _AB	=	bulk density
N _AB	=	total number of atoms A and B in the system
K	=	number of time steps
δ _r	=	distance interval
ΔN _AB	=	number of B (or A) atoms between r and δr around an A (or B) atom^53,134

In RDF, the position and intensity of the first emerged peak is of the utmost importance. The peaks which appear at shorter distance and have higher intensity and suggest higher interactions.

RDF can be used to study the interaction not only between the hard segments but also between the hard and soft segments. The RDF of hydrogen connected to nitrogen with nitrogen or oxygen atom of hard segments (N-H…N-H and N-H…O=C) illustrates the hard segment interactions. Whereas the RDF of hydrogen connected to nitrogen with oxygen of soft segments (N-H…O-C and N-H…O=C) corroborates the hard and soft segment interactions.

Moreover, MD can calculate Flory-Huggins parameter. As mentioned before, this value is a strong criterion to determine the probability of the phase separation.

MD interaction parameter is calculated from equation (33)

χ_{M D} = \frac{z Δ ε}{K_{B} T}

(33)

where

z	=	lattice coordination number
Δε	=	excess exchange interaction energy
K _B	=	Boltzmann constant
T	=	absolute temperature

MD = calculates the Δε value for an equilibrated cell.¹³⁵

MD predicts the diffusion coefficient of soft and hard segments using the mean square displacement (equations (34) and (35))

M S D (t) = \frac{1}{N} \sum_{i = 1}^{N} 〈 {| r_{i} (t) - r_{i} (0) |}^{2} 〉

(34)

D_{M D} = \frac{1}{6 N} \lim_{t \to \infty} \frac{d}{d t} \sum_{i = 1}^{N} 〈 {| r_{i} (t) - r_{i} (0) |}^{2} 〉

(35)

where

ri(t)	=	atom position at time t
ri (0)	=	atom position at time t = 0
N	=	number of diffusive atoms^136,137

Diffusion coefficient can indirectly signify the extent of phase separation. Higher phase separation gives rise to the lower diffusion coefficient for the hard segments.⁵⁰ Because with increased phase separation, the interaction between hard segments is increased and the hard segments mobility is decreased. On the other hand, higher phase separation results in higher soft segment diffusion coefficient. Because with increased phase separation, the interaction between hard and soft segments decrease and soft segments become more mobile.

In summary, the higher the phase separation, the lower the diffusion coefficient of the hard segments and the higher the diffusion coefficient of the soft segment will be.

Moreover, MD has ability to calculate the solubility parameters of the molecules. In this regard, the solubility parameter of the individual hard or soft segments as well as that of resulting polymer can be calculated by the equation (36)

δ_{M D} = \sqrt{E_{C E D}}

(36)

where E_CED is given by equation (37)

E_{C E D} = \frac{(U_{v d w} + U_{Q})}{V}

(37)

where

U _vdw	=	van der Waals energy
U _Q	=	electrostatic energy¹³⁸

The difference between solubility parameter for hard and soft segments determines how much the segments will separate. The higher solubility parameter difference suggests higher phase separation. Moreover, the PUs with higher solubility parameter generally undergoes lower phase separation. Table 1 presents different methods for studying PU phase separation.

Table 1.

Different methods for study of the PU phase separation.

Approach	Methodology	Measured parameters	Advantages and disadvantages	References
Transparency measurement	Measuring the sample optical transmission at 500 nm, lower transmission corresponds to phase separation	Degree of phase separation	Advantages: Simple, inexpensive	⁸²
Transparency measurement		Degree of phase separation	Disadvantages: Limited to phase separation degree measurement, lacks high accuracy	⁸²
Fourier-transform infrared spectroscopy (FTIR)	Measuring the vibrations arise from the hydrogen bonded and non-hydrogen bonded N-H or C=O moieties, normalizing the intensity of the hydrogen bonded groups to those of non-hydrogen bonded ones corresponds to phase separation degree	Degree of phase separation	Advantages: Simple, conventional	^78,101,102
Fourier-transform infrared spectroscopy (FTIR)		Degree of phase separation	Disadvantages: Measuring phase separation with some negligence, limited to phase separation degree, lacks high accuracy	^78,101,102
Nuclear magnetic resonance spectroscopy (NMR)	Studying the ¹H chemical shifts of NH group and¹³C chemical shifts of C=O provides the information of hydrogen bonds between either soft-hard and hard-hard segments and thus the extent of phase separation	Degree of phase separation, size of hard domains, thickness of interphase	Advantages: Measuring the phase separation extent, hard domain size and interphase thickness, very high accuracy	^{103–105,109}
Nuclear magnetic resonance spectroscopy (NMR)			Disadvantages: Expensive, not easily accessible, difficult data analysis	^{103–105,109}
Rheometrics mechanical spectrometer (RMS)	Measuring the phase separation temperature from time sweep analysis in a point that a sharp increase of storage modulus occurs, measuring the extent of phase separation from the storage modulus at the beginning and end of the time sweep analysis	Extent of phase separation, temperature and time of phase separation	Advantages: Relatively inexpensive and precise, measuring the time and extent of phase separation	37,38,51
Rheometrics mechanical spectrometer (RMS)			Disadvantages: Not as accurate as solid-state NMR	37,38,51
Differential scanning calorimetry (DSC)	Calculates the degree of phase separation from the increase of specific heat capacity at T_g	Degree of phase separation, weight fraction of soft and hard phases	Advantages: Calculates the phase separation degree, weight fraction and Tg of soft and hard phases, low amount of the needed sample, relatively high accuracy	^45,46,139
Differential scanning calorimetry (DSC)		T_g of hard and soft phases	Disadvantages: Not as accurate as solid-state NMR	^45,46,139
Small angle X-ray scattering (SAXS)	Obtains structural information from the X-ray collision with sample, scattering peak in PUs corresponds to local heterogeneities in the electron density of the phase separated domains	Extent of phase separation, inter-domain distances and domain boundary diffuseness	Advantages: Measures the phase separation extent, inter-domain distances and domain boundary diffuseness, very accurate and comprehensive	^{47,48,120,122}
Small angle X-ray scattering (SAXS)			Disadvantages: Relatively difficult data analysis, possible damages to instrument for polar materials	^{47,48,120,122}
Theoretical approaches	Provides an insight into the probability of phase separation by calculating polymer interaction parameter as well as soft and hard segment solubility parameters, the interaction parameter to critical interaction parameter ratio corresponds to the extent of phase separation	Extent of phase separation	Advantages: Predicting the probability and the extent of phase separation	^51,67
Theoretical approaches		Extent of phase separation	Disadvantages They should be combined with experimental finding to give a useful information	^51,67
Molecular dynamics (MD) simulation	Analyzes the equilibrated cell loaded with PU chains of desired hard and soft segments moieties and calculates the cell parameters, the position and intensity of the emerged RDF peaks of MD corresponds to the extent of interactions between the segments	Possibility of phase separation	Advantages: Study the molecular interactions between hard and soft segments and phase separation extent, decrease the cost and time needed for the extended experimental studies.	^9,51,53
Molecular dynamics (MD) simulation		Possibility of phase separation	Disadvantages MD simulation should be confirmed with experimental analyses	^9,51,53

Conclusion

Phase separation can be studied by experimental, theoretical and computer modeling and simulation approaches. The experimental approaches evaluate the phase separation with respect to chemical, rheological, thermal and structural facets.

Transparency measurement evaluates the PU phase separation by measuring light transmission. The homogeneous phases produce transparent samples, while the phase-separated phases decrease the light transmission and give rise to opacity. Transparency measurement is very simple and convenient; however, it is not a very precise method for studying PU phase separation. Moreover, it only provides data on phase separation extent.

FTIR measures the phase separation based on the hydrogen bonding between urethane groups. Although FTIR is a simple and accepted method for measuring PU phase separation, it cannot perfectly represent the microphase separation level. Because in this method, the N-H or C=O moieties of the urethane group in interphase may not form hydrogen bonds. Besides, all carbonyl or amine functionalities in hard domains cannot make hydrogen bonds; therefore, they are neglected from the measurement.

Solid-state NMR is an excellent method for evaluating PU phase separation. Solid-state NMR is able to measure not only the extent of phase separation but also the size of hard domain and the thickness of interphase for different morphology of the phase-separated structure (i.e., lamellar, cylindrical and spherical morphologies). However, this technique is expensive and is not easily accessible. Moreover, the data analysis of NMR is complicated and should be down by a specialist.

Rheological analysis is a very interesting approach for measuring not only the extent but also the phase separation temperature and time. The rheological analyses can be conducted by a parallel plate or cone and plate rheometer. This method overcomes the disadvantages mentioned above. It is a relatively inexpensive and precise method and its data analysis is not very complicated.

DSC is one of the most practical approaches for evaluating the PU phase separation. This method calculates not only the degree of phase separation but also the weight fraction and T_g of the soft segment and hard segment rich phases. DSC is a very acceptable approach to study PU phase separation due to its long history in this field, small sample needed and high accuracy.

SAXS is a useful method to measuring PU phase segregation. It can measure the extent of phase separation, inter-domain distances and domain boundary diffuseness. This technique is very accurate and comprehensive; however, its data analysis is somewhat complicated. Moreover, for polar components, the components may adhere to SAXS tube and damage the instrument in frequent usages.

In addition to experimental analyses, theoretical bases can be used to realize the probability and the extent of PU phase segregation. The theoretical approaches provide an insight into the probability of phase separation with the calculation of polymer interaction parameter as well as soft and hard segment solubility parameters. Theoretical studies are very interesting; however, they should be combined with experimental finding to give useful information. MD simulation predicts the extent of molecular interactions between hard and soft segments and thus the extent of phase separation by representing the pair correlation function. Like the theoretical studies, MD simulation should be confirmed with the experimental analyses. Indeed, the most important difference between different methods is their accuracy. Each method evaluates the phase separation with a special precision.

In this paper, several approaches for evaluating the PU phase separation have been reviewed. However, a clear and comprehensive interpretation of the PU phase separation and morphology of the separated domains cannot be achieved by the one approach and a combination of methods should be used to deliver enough information of PU microphase separation. Moreover, using more advanced techniques including electron spin resonance (ESR) can better shed light on PU phase separation. ESR is basically similar to NMR, with this difference that the excitation occurs for electron spins instead of nucleus spins.¹⁴⁰

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Vahid Haddadi-Asl

Biographies

Mehdi Gholami is a MSC student in Amirkabir University of technology. His field of research is 3D printing of polymers.

Vahid Haddadi-Asl is a full professor in Amirkabir University of technology. His field of research includes polyurethane, modeling, biomaterials, tissue engineering, and drug delivery. He has numerous papers in these fields.

Iman Sahebi Jouibari is a researcher who finished his PhD at Amirkabir University in 2019. His fields of research are polyurethane and modeling and he has several research papers in these fields.