# The Influence of Water and Solvent Uptake on Functional Properties of Shape-Memory Polymers

Authors: Ehsan Ghobadi; Axel Marquardt; Elias Mahmoudinezhad Zirdehi; Klaus Neuking; Fathollah Varnik; Gunther Eggeler; Holger Steeb
Journal: International Journal of Polymer Science
 (2018)

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## Abstract

In this contribution, diffusion of water, acetone, and ethanol into a polymer matrix has been studied experimentally and numerically by finite element approaches. Moreover, the present study reports an assessment of different thermomechanical conditions of the shape-memory (SM) performance, for example, stress- or strain-holding times in stress- or strain-controlled thermomechanical cycles and the effect of maximum strain. According to the results presented here, the uptake of acetone in Estane is much higher than ethanol and follows classical Fickian diffusion. Further, a series of thermomechanical measurements conducted on dry and physically (hydrolytically) aged polyether urethanes revealed that incorporation of water seems to have an appreciable impact on the shape recovery ratios which can be attributed to the additional physical crosslinks. However, no obvious difference in shape fixation of dry and physically (hydrolytically) aged samples could be recognized. Furthermore, by decreasing the strain-holding time, shape recovery improves significantly. Moreover, the shape fixity is found to be independent of holding time. The shape recovery ratio decreased dramatically with an increase in the stress-holding time.


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## Body

## 1. Introduction

The thermally induced shape-memory effect (SME) of a system is an ability to maintain a temporarily fixed deformation that is established after the application of a specific thermomechanical treatment called programming [1]. Such programmed polymers can shift back to their original shape, when exposed to heat and pass a certain temperature called transition temperature (θsw) [1]. The temperature θsw is related to the thermal transition of switching domains and can be the glass (θg) or the melting temperature (θm) [2]. Such programming procedure consists of three steps: (I) heating and deforming above θsw, (II) cooling to θ<θsw to solidify the switching domains, and (III) unloading at this temperature to obtain a programmed fixed shape [3]. The recovery of a SMP is performed by entropy acquirement of switching domains, when moving from an oriented (programmed) configuration to a random coil (recovered) chain conformation by heating to θ>θsw [4].Functional properties of SMPs are normally studied by cyclic thermomechanical tests [5, 6]. Characteristic functional properties for the quantification of the SME are the shape fixity ratio (Rf) and the shape recovery ratio (Rr). Rf describes the capability of a polymer to temporarily fix an applied deformation, whereas Rr expresses how well the original shape is recovered.Several parameters can alter the functional properties of polymers. Among them are, for example, the maximum strains during programming or the holding time after deformation. It was observed that the functional properties of thermally induced SMPs can also be significantly affected or even triggered by the uptake of solvents [7–10]. This can lead to chemical or physical aging [11–13]. Influencing the functional properties of SMPs through chemical aging is irreversible. In such processes, the chemical structure of the system is irreversibly changed, for example, in hydrolytically degraded polymers [13, 14]. In contrast, physical aging occurs when the molecular structure of the polymer does not change. Physical aging is reversible, so that the physically aged sample can be brought back to its initial state with some measures, for example, heating and drying [15].The shape-memory capability of a system in vicinity to humidity or solvents can be strongly changed, before, during, and after programming [16, 17]. For instance, the worsening of shape recovery of a programmed polymer is an effect of physical aging because of humidity uptake which starts right after the first day of keeping them at a temperature lower than their glass transition temperature (θg) that may cause an incomplete, premature loss of the programmed shape [18]. This is the main reason why SMPs have a certain lifetime and have to be stored and maintained under particular conditions [19].The observation that humidity can substantially influence the functional properties of SMPs has gained abundant attraction in recent years and is of great relevance for numerous medical applications [20, 21]. This has motivated the development of moisture-triggered SME [16–18]. The fundamental mechanisms of moisture triggering are either destabilization and elimination of hydrogen bonds [9], water-induced dissolution of crystalline domains [22], or degradation of switching domains responsible for shape fixation and recoiling of the chain segments during recovery [7].Although accidental life-altering processes of polymers through physical or chemical aging are not prepossessing and desirable,targeted aging of materials before practical applications is required. Therefore, one important question is how functional properties of a SMP change, if it is “meaningfully” and “targeted” aged before programming (e.g., by introducing solvent molecules into the polymer matrix)? To our best knowledge, there is no systematic research to answer this question. Therefore, the aim of this study is to explore, whether targeted physical aging “prior to programming” can influence the functional properties of a commercially available polyether urethane (Estane, Lubrizol, Ovele Westerlo, Belgium). For this reason, dry and physically aged samples have been prepared. Physical aging was performed through the uptake of three different solvents: acetone (C3H6O), ethanol (C2H6O), and water (H2O), and their sample-specific transport behavior was numerically studied. Moreover, the related changes in θg were discussed experimentally and numerically by molecular dynamics (MD) simulations.It was observed that the incorporation of the above-mentioned solvents into the polymer matrices significantly changed the shape-memory capability of Estane. However, in the present contribution, only the results for hydrolytically (physically) aged samples will be discussed. This is because of the fact that the amount of diffused acetone and ethanol in the polymer samples at the single steps of the shape-memory cycle could not be controlled, so that at the end of experiments unpredicted desorption effects have been observed and the data were not reproducible. For water-swollen samples, on the other hand, no significant mass change was detected.Following the previous studies with Estane [23] and experimental water sorption investigations performed here, a maximum mass gain of 3 wt.% to 3.1 wt.% can be expected.For the quantification of functional properties of Estane, cyclic thermomechanical tests consisting of two subsequent cycles with a uniaxial strain ofεm=10% was applied for dry and hydrolytically aged samples. Additionally, the same procedure was repeated with different holding times and with different maximum strains of εm=30%, 60%, 100%, and 150% for both dry and hydrolytically aged samples.


## 2. Materials and Methods

### 2.1. Materials

In the present contribution, aliphatic SM-polyurethane Estane (designation: ETE75DT3 NAT022) granulates (Lubrizol, Ovele Westerlo, Belgium) have been processed using an injection molding machine (Arburg Allrounder 270M 500-210, Lossburg, Germany). Processing steps and detailed sample preparation stages have been explained in [24, 25]. Molecular weight and weight distribution of Estane have been determined by Gel permeation chromatography, and results can be found in Supplement I. Fig. S1 shows size-exclusion gel permeation chromatography analysis of Estane. Here, an average molecular weight of 126 kg/mole was determined.For solvent uptake and physical aging operations, three different solvents have been used: deionized water H2O (HPLC grade, VWR Chemicals, Darmstadt, Germany), ethanol C2H6O (analytical reagent grade, absolute 99.8 + %, certificated for analysis, Fisher Scientific UK), and acetone C3H6O (analytical reagent grade, certificated for analysis, Fisher Scientific UK).


### 2.2. Numerical Investigations

Numerical investigations of Fickian diffusion have been studied with the commercial Finite Element software package COMSOL 5.0 Multiphysics.Modeling theθg of dry and physically (hydrolytically) aged polymer samples has been performed through MD simulations with the MD software package LAMMPS, developed at Sandia National Laboratories [26]. Here, a generic model of a polymer with a finite extensible nonlinear elastic (FENE) potential has been employed, which allows to focus on generic rather than material-specific aspects. All simulations were performed in an NPT (number of molecules, pressure, and temperature constant) ensemble using Nose-Hoover thermostat and barostat to apply desired temperature and pressure. The equations of motions are integrated with the velocity Verlet algorithm.The presented atomistic model is built up of 156 chains of 64-bead length, along with various numbers of small particles. The nonbonded interactions are modeled by the Lennard-Jones (LJ) potentialUαβLJ, and the connectivity of covalent bonds along the chains is ensured via the FENE potential UFENE as follows:
(1)UFENE=−12KR02ln1−rR02,UαβLJ=4ϵαβσαβrαβ12−σαβrαβ6,where ϵαβ, σαβ, rαβ, k=30ϵpp/σpp2, r, and R0=1.5σpp are the van der Waals (vdW) potential strength, the distance with zero potential energy, interatomic distance, strength factor of bonded potential, covalent bond length, and the breaking limit of the bonds, respectively. It should be noted that α,β∈p,s and p and s stand for polymer and small molecules (solvents), respectively. The quantity σpp is chosen to equal to 1, and the size of small particles is adjusted by setting σss=0.5σpp. The quantity σps is obtained by the arithmetic mean of σpp and σss.Figure1(a) shows a schematic view of the chain segment of the polymer in the vicinity of solvent molecules. As depicted in this picture, the distances between atoms of polymers and solvents are represented with rpp, rsp, and rss, where rpp is the distance between atoms of polymers, rps between atoms of polymers and solvents, and rss between atoms of solvents, respectively. Moreover, in Figure 1(b), a snapshot of the simulation box is also shown. For the construction of initial polymer chains, the monomers are placed regularly on a 3D grid after which the system is melted at a relatively high temperature of θ=2 (θg=0.44 for the present model and all quantities in LJ units) to achieve statistically random distributions of chain conformations. It should be noted that for the sake of data interpretation, three independent packing models were built and simulations were performed for all three samples. The results shown here are an average out of three.Figure 1
(a) A schematic view of the model used in the MD simulations. (b) A snapshot of the simulation box containing polymers and small molecules. Different chains are shown with different colors to improve visibility. Small molecules appear as small red spherical particles.
(a)
(b)


### 2.3. Experimental Sorption and Diffusion Studies

Prior to any experiment, the injection-molded plates of Estane with a thickness 2 mm have been kept in a vacuum desiccator to keep them dry. Afterwards, the plates were cut to round discs of diameter 44.5 mm with a mass of 3.777 ± 0.017 g. For sorption and diffusion experiments, these plates were positioned in reaction vessels containing 200 ml of water, ethanol, or acetone. The temperature of the reaction vessels has been controlled through a temperature-controlled water bath. Afterwards, each specimen was dried carefully dabbing the wet surfaces with a wad of lint-free cotton wool and then reimmersed into the reaction vessel. It should be noted that the measuring time was kept below 30 s to keep evaporation processes at a minimum. Moreover, weights were measured using an analytical balance of a type Sartorius A200S (Göttingen, Germany; resolution: 0.1 mg). The weight gain during sorption experiments is described as the solvent mole uptake bymp=100 g of polymer:
(2)ct=msMs×mp×100%,where ms is the mass of sorbed solvent and Ms is its molar mass and mp denotes the mass of the polymer.


### 2.4. Thermorheological Characterization

Using rectangular samples with dimensions of W × H × L: 2 × 10 × 50 mm3, dynamic mechanical thermal analysis (DMTA) experiments were accomplished in torsion mode with a stress-controlled rheometer with integrated Peltier-based temperature chamber (Anton Paar Physica MCR 301 plus CTD 180, Graz, Austria). During the torsion DMTA tests, a small uniaxial tensile force of around 0.5 N is superimposed to maintain the specimen under net tension. Thereupon, harmonic twist rotations with prescribed amplitude (0.01%) and constant frequency of 10 Hz were executed while the samples were heated in predefined temperature intervals at a constant heating rate of 0.25°C/min and the resulting harmonic torque as well as the phase lag ϕ or loss factor tan ϕ was measured. Such temperature sweep experiments provide important insights into the effective viscoelastic properties of the investigated material [27]. Here, the characteristic material properties like θg can be determined through the sample’s response to the applied periodic loadings. Again here, the experiments have been repeated two more times and the results originate from an average out of all three runs.


### 2.5. Cyclic, Thermomechanical Tensile Tests

For tensile tests, Estane sheets were punched to dumbbell specimens of type 5A of DIN EN ISO 527-2 (W × H × L: 2 × 10 × 75 mm3). The gauge length of specimens is 25 mm. Cyclic, thermomechanical tensile tests were performed on a spindle-driven testing machine (Schenck Trebel RM50, Germany) with an adjusted strain and compression capacity of ±500 N. The machine was equipped with a heating/cooling chamber (Fresenberger TK18.400.100, Wipperfürth, Germany). The temperature was PID-controlled (Eurotherm 3508, Limburg, Germany) so that temperatures in the range of −100 to 400°C could be adjusted and kept constant with a precision of ±1°C. Each cycle consisted of a SM creation procedure (SMCP) under strain-controlled modes and recovery modes. In the programming part, the samples were heated up from room temperature to the upper working temperature of θhigh=70°C with a moderated heating rate of 3°C/min. Following that, temperature θhigh was fixed and, in a strain-controlled mode, the samples were deformed up to the maximum uniaxial strain of εm at a rate of 0.0051/s. Subsequently, the deformed specimens were kept constant at θhigh for different holding times th. Under constant strain conditions, the specimens were then cooled down to a lower temperature of θlow=10°C with a cooling rate of 3°C/min and equilibrated for 40 min. Afterwards, the temporarily fixed strains εu were achieved along with the removal of stress. Under stress-free conditions, the recovery parts were induced by heat up of the programmed samples to θhigh=70°C with the same heating rate as mentioned before and equilibrated for 40 min. Finally, the shape fixity and shape recovery ratios were measured for the quantification of the SME. Figure 2 demonstrates all steps of the thermomechanical tensile test cycle in a stress-temperature-stain (σ-θ-ε) diagram. These five steps of a cyclic uniaxial thermomechanical tensile test are based on strain-controlled programming and a stress-free recovery procedure. It should be noted that the thermomechanical tensile test was repeated once more (N=2). However, only the results of the second cycle have been used for data interpretation, as the first cycle was utilized to erase the history of the system [28]. The results for the first cycle can be found in Supplement I. The following 2nd cycle could allow two different strain regimes with respect to the previous cycle (N=1) in which the samples were stretched in a strain-controlled setting up to the maximum strain εm. In subsequent thermomechanical tensile tests (N>1), the sample in a strain-controlled process can be stretched up to the previous maximum strain εm2=εm1−εu2, which is called strain length approach. Comparatively, it can be stretched with additional previous maximum strains εm2=εm1. This approach is called subsequent additional strain [29]. In this contribution, samples have been stretched in the second cycle up to εm2 according to strain length approach. These experiments have also been performed three times, and the results descend from the average out of them.Figure 2
Schematic representation of a cyclic uniaxial thermomechanical tensile test in theσ-θ-ε diagram.For the quantification of the SME of polymer samples, the shape fixity ratioRfN and shape recovery ratio RrN have been determined as important functional properties of the system. The shape fixity ratio RfN is the ratio of the strain in a stress-free state after removing the tensile stress in the Nth cycle εuN and the maximum strain εmN. The shape recovery ratio RrN is on the other hand the ratio between the remaining strain after the Nth cycle to the remaining strain in the previous cycle and can be determined from strain values according to
(3)Rf=εuNεm×100%,Rr=εm−εpNεm−εpN−1×100%.Here,εpN is the recovered strain of the sample at the end of the recovery step.


### 2.6. Study of Diffusion Behavior

If the mode of diffusion is of Fickian type, then the diffusion rates of small molecules are faster than the relaxation process of polymer chains [30]. According to Fick’s 1st law, moisture sorption occurs only by diffusion and the diffusion flux jx,t is directly proportional to the gradient of its concentration:
(4)j=−Dgradc,where cx,t is the sorbent concentration with units mol/m3 and D is the (isotropic) diffusion coefficient or diffusivity of a homogenous sample with units of m2/s. The process of diffusion into the sample has therefore the following form:
(5)divj+α∂c∂t=0,(6)α∂c∂t−Ddivgradc=0.To determine the changes of concentration of sorbents inside the sample at each point and time, (6) should be solved with respect to boundary conditions:
(7)c=c¯,∀c¯∈ΓD×t,j⋅n=j¯,∀j¯∈ΓN×t,at the Neumann boundary ΓN and the Dirichlet boundary ΓD and initial conditions in the sample’s domain Ω at t=t0:
(8)c=c0,∀c0∈Ω×t0.Multiplying diffusion Equation (6) with a test function (δc) and integrating by parts over the domain of the sample leads to the weak form:
(9)∫Ωα∂tcδcdV+∫ΩDgradc⋅gradδcdV=∫ΓNj¯δc.Equation (9) is discretized with standard (Lagrangian) finite elements in the spatial domain. Applying an implicit backward Euler time stepping scheme, it could be solved numerically and the evolution of concentration cx,t can be analyzed for different sample geometries. Here, we investigate the mentioned samples of dimensions W × H × L: 2× 10 × 50 mm3. The temporal concentration changes of the center of the mass of the sample have been recorded for three different probe molecules: acetone, ethanol, and water.In addition to sorption, permeability is also important. The transport of small molecules inside polymers occurs through a solution-diffusion mechanism. This means that small molecules are first sorbed by the sample and then diffused inside it. The total amount of diffusion depends upon the existing number of probe molecules between two successive layers. For this reason, isotropic permeabilityζ is introduced as
(10)ζ=DS,where S is the solubility parameter with the unit of pascal1/2.In addition to numerical solution of diffusivity, the diffusion coefficientD can be calculated by a 1-dimensional analytical solution after an appropriate mathematical computation. A well-known analytical solution of cx for a 1-dimensional boundary value problem solution is developed by Crank [31], which is the most suitable for moderate and long-term experiments. More details about the numerical solution of Fick’s law can be found in Supplement I Section S2.


## 2.1. Materials

In the present contribution, aliphatic SM-polyurethane Estane (designation: ETE75DT3 NAT022) granulates (Lubrizol, Ovele Westerlo, Belgium) have been processed using an injection molding machine (Arburg Allrounder 270M 500-210, Lossburg, Germany). Processing steps and detailed sample preparation stages have been explained in [24, 25]. Molecular weight and weight distribution of Estane have been determined by Gel permeation chromatography, and results can be found in Supplement I. Fig. S1 shows size-exclusion gel permeation chromatography analysis of Estane. Here, an average molecular weight of 126 kg/mole was determined.For solvent uptake and physical aging operations, three different solvents have been used: deionized water H2O (HPLC grade, VWR Chemicals, Darmstadt, Germany), ethanol C2H6O (analytical reagent grade, absolute 99.8 + %, certificated for analysis, Fisher Scientific UK), and acetone C3H6O (analytical reagent grade, certificated for analysis, Fisher Scientific UK).


## 2.2. Numerical Investigations

Numerical investigations of Fickian diffusion have been studied with the commercial Finite Element software package COMSOL 5.0 Multiphysics.Modeling theθg of dry and physically (hydrolytically) aged polymer samples has been performed through MD simulations with the MD software package LAMMPS, developed at Sandia National Laboratories [26]. Here, a generic model of a polymer with a finite extensible nonlinear elastic (FENE) potential has been employed, which allows to focus on generic rather than material-specific aspects. All simulations were performed in an NPT (number of molecules, pressure, and temperature constant) ensemble using Nose-Hoover thermostat and barostat to apply desired temperature and pressure. The equations of motions are integrated with the velocity Verlet algorithm.The presented atomistic model is built up of 156 chains of 64-bead length, along with various numbers of small particles. The nonbonded interactions are modeled by the Lennard-Jones (LJ) potentialUαβLJ, and the connectivity of covalent bonds along the chains is ensured via the FENE potential UFENE as follows:
(1)UFENE=−12KR02ln1−rR02,UαβLJ=4ϵαβσαβrαβ12−σαβrαβ6,where ϵαβ, σαβ, rαβ, k=30ϵpp/σpp2, r, and R0=1.5σpp are the van der Waals (vdW) potential strength, the distance with zero potential energy, interatomic distance, strength factor of bonded potential, covalent bond length, and the breaking limit of the bonds, respectively. It should be noted that α,β∈p,s and p and s stand for polymer and small molecules (solvents), respectively. The quantity σpp is chosen to equal to 1, and the size of small particles is adjusted by setting σss=0.5σpp. The quantity σps is obtained by the arithmetic mean of σpp and σss.Figure1(a) shows a schematic view of the chain segment of the polymer in the vicinity of solvent molecules. As depicted in this picture, the distances between atoms of polymers and solvents are represented with rpp, rsp, and rss, where rpp is the distance between atoms of polymers, rps between atoms of polymers and solvents, and rss between atoms of solvents, respectively. Moreover, in Figure 1(b), a snapshot of the simulation box is also shown. For the construction of initial polymer chains, the monomers are placed regularly on a 3D grid after which the system is melted at a relatively high temperature of θ=2 (θg=0.44 for the present model and all quantities in LJ units) to achieve statistically random distributions of chain conformations. It should be noted that for the sake of data interpretation, three independent packing models were built and simulations were performed for all three samples. The results shown here are an average out of three.Figure 1
(a) A schematic view of the model used in the MD simulations. (b) A snapshot of the simulation box containing polymers and small molecules. Different chains are shown with different colors to improve visibility. Small molecules appear as small red spherical particles.
(a)
(b)


## 2.3. Experimental Sorption and Diffusion Studies

Prior to any experiment, the injection-molded plates of Estane with a thickness 2 mm have been kept in a vacuum desiccator to keep them dry. Afterwards, the plates were cut to round discs of diameter 44.5 mm with a mass of 3.777 ± 0.017 g. For sorption and diffusion experiments, these plates were positioned in reaction vessels containing 200 ml of water, ethanol, or acetone. The temperature of the reaction vessels has been controlled through a temperature-controlled water bath. Afterwards, each specimen was dried carefully dabbing the wet surfaces with a wad of lint-free cotton wool and then reimmersed into the reaction vessel. It should be noted that the measuring time was kept below 30 s to keep evaporation processes at a minimum. Moreover, weights were measured using an analytical balance of a type Sartorius A200S (Göttingen, Germany; resolution: 0.1 mg). The weight gain during sorption experiments is described as the solvent mole uptake bymp=100 g of polymer:
(2)ct=msMs×mp×100%,where ms is the mass of sorbed solvent and Ms is its molar mass and mp denotes the mass of the polymer.


## 2.4. Thermorheological Characterization

Using rectangular samples with dimensions of W × H × L: 2 × 10 × 50 mm3, dynamic mechanical thermal analysis (DMTA) experiments were accomplished in torsion mode with a stress-controlled rheometer with integrated Peltier-based temperature chamber (Anton Paar Physica MCR 301 plus CTD 180, Graz, Austria). During the torsion DMTA tests, a small uniaxial tensile force of around 0.5 N is superimposed to maintain the specimen under net tension. Thereupon, harmonic twist rotations with prescribed amplitude (0.01%) and constant frequency of 10 Hz were executed while the samples were heated in predefined temperature intervals at a constant heating rate of 0.25°C/min and the resulting harmonic torque as well as the phase lag ϕ or loss factor tan ϕ was measured. Such temperature sweep experiments provide important insights into the effective viscoelastic properties of the investigated material [27]. Here, the characteristic material properties like θg can be determined through the sample’s response to the applied periodic loadings. Again here, the experiments have been repeated two more times and the results originate from an average out of all three runs.


## 2.5. Cyclic, Thermomechanical Tensile Tests

For tensile tests, Estane sheets were punched to dumbbell specimens of type 5A of DIN EN ISO 527-2 (W × H × L: 2 × 10 × 75 mm3). The gauge length of specimens is 25 mm. Cyclic, thermomechanical tensile tests were performed on a spindle-driven testing machine (Schenck Trebel RM50, Germany) with an adjusted strain and compression capacity of ±500 N. The machine was equipped with a heating/cooling chamber (Fresenberger TK18.400.100, Wipperfürth, Germany). The temperature was PID-controlled (Eurotherm 3508, Limburg, Germany) so that temperatures in the range of −100 to 400°C could be adjusted and kept constant with a precision of ±1°C. Each cycle consisted of a SM creation procedure (SMCP) under strain-controlled modes and recovery modes. In the programming part, the samples were heated up from room temperature to the upper working temperature of θhigh=70°C with a moderated heating rate of 3°C/min. Following that, temperature θhigh was fixed and, in a strain-controlled mode, the samples were deformed up to the maximum uniaxial strain of εm at a rate of 0.0051/s. Subsequently, the deformed specimens were kept constant at θhigh for different holding times th. Under constant strain conditions, the specimens were then cooled down to a lower temperature of θlow=10°C with a cooling rate of 3°C/min and equilibrated for 40 min. Afterwards, the temporarily fixed strains εu were achieved along with the removal of stress. Under stress-free conditions, the recovery parts were induced by heat up of the programmed samples to θhigh=70°C with the same heating rate as mentioned before and equilibrated for 40 min. Finally, the shape fixity and shape recovery ratios were measured for the quantification of the SME. Figure 2 demonstrates all steps of the thermomechanical tensile test cycle in a stress-temperature-stain (σ-θ-ε) diagram. These five steps of a cyclic uniaxial thermomechanical tensile test are based on strain-controlled programming and a stress-free recovery procedure. It should be noted that the thermomechanical tensile test was repeated once more (N=2). However, only the results of the second cycle have been used for data interpretation, as the first cycle was utilized to erase the history of the system [28]. The results for the first cycle can be found in Supplement I. The following 2nd cycle could allow two different strain regimes with respect to the previous cycle (N=1) in which the samples were stretched in a strain-controlled setting up to the maximum strain εm. In subsequent thermomechanical tensile tests (N>1), the sample in a strain-controlled process can be stretched up to the previous maximum strain εm2=εm1−εu2, which is called strain length approach. Comparatively, it can be stretched with additional previous maximum strains εm2=εm1. This approach is called subsequent additional strain [29]. In this contribution, samples have been stretched in the second cycle up to εm2 according to strain length approach. These experiments have also been performed three times, and the results descend from the average out of them.Figure 2
Schematic representation of a cyclic uniaxial thermomechanical tensile test in theσ-θ-ε diagram.For the quantification of the SME of polymer samples, the shape fixity ratioRfN and shape recovery ratio RrN have been determined as important functional properties of the system. The shape fixity ratio RfN is the ratio of the strain in a stress-free state after removing the tensile stress in the Nth cycle εuN and the maximum strain εmN. The shape recovery ratio RrN is on the other hand the ratio between the remaining strain after the Nth cycle to the remaining strain in the previous cycle and can be determined from strain values according to
(3)Rf=εuNεm×100%,Rr=εm−εpNεm−εpN−1×100%.Here,εpN is the recovered strain of the sample at the end of the recovery step.


## 2.6. Study of Diffusion Behavior

If the mode of diffusion is of Fickian type, then the diffusion rates of small molecules are faster than the relaxation process of polymer chains [30]. According to Fick’s 1st law, moisture sorption occurs only by diffusion and the diffusion flux jx,t is directly proportional to the gradient of its concentration:
(4)j=−Dgradc,where cx,t is the sorbent concentration with units mol/m3 and D is the (isotropic) diffusion coefficient or diffusivity of a homogenous sample with units of m2/s. The process of diffusion into the sample has therefore the following form:
(5)divj+α∂c∂t=0,(6)α∂c∂t−Ddivgradc=0.To determine the changes of concentration of sorbents inside the sample at each point and time, (6) should be solved with respect to boundary conditions:
(7)c=c¯,∀c¯∈ΓD×t,j⋅n=j¯,∀j¯∈ΓN×t,at the Neumann boundary ΓN and the Dirichlet boundary ΓD and initial conditions in the sample’s domain Ω at t=t0:
(8)c=c0,∀c0∈Ω×t0.Multiplying diffusion Equation (6) with a test function (δc) and integrating by parts over the domain of the sample leads to the weak form:
(9)∫Ωα∂tcδcdV+∫ΩDgradc⋅gradδcdV=∫ΓNj¯δc.Equation (9) is discretized with standard (Lagrangian) finite elements in the spatial domain. Applying an implicit backward Euler time stepping scheme, it could be solved numerically and the evolution of concentration cx,t can be analyzed for different sample geometries. Here, we investigate the mentioned samples of dimensions W × H × L: 2× 10 × 50 mm3. The temporal concentration changes of the center of the mass of the sample have been recorded for three different probe molecules: acetone, ethanol, and water.In addition to sorption, permeability is also important. The transport of small molecules inside polymers occurs through a solution-diffusion mechanism. This means that small molecules are first sorbed by the sample and then diffused inside it. The total amount of diffusion depends upon the existing number of probe molecules between two successive layers. For this reason, isotropic permeabilityζ is introduced as
(10)ζ=DS,where S is the solubility parameter with the unit of pascal1/2.In addition to numerical solution of diffusivity, the diffusion coefficientD can be calculated by a 1-dimensional analytical solution after an appropriate mathematical computation. A well-known analytical solution of cx for a 1-dimensional boundary value problem solution is developed by Crank [31], which is the most suitable for moderate and long-term experiments. More details about the numerical solution of Fick’s law can be found in Supplement I Section S2.


## 3. Results and Discussions

### 3.1. Diffusion Behavior of Small Molecules into Estane Samples

The Fickian conduct of acetone, ethanol, and water inside Estane is studied at different temperatures experimentally and by the mean of finite element simulations. Since the qualitative behavior of the diffusion processes of the mentioned solvents into Estane is similar, only the results for acetone are shown here.The simulation results for the temporal evolution of the concentration of acetone in the middle of the sample (W × H × L: 2 × 10 × 50 mm3) for different temperatures modeled are shown in Figure 3. As can be recognized from this picture, the amount of acetone molecules which are diffused inside the sample, increases with temperature and the concentration profile has a biphasic form. Below θg, the increase of acetone concentration is clearly lower than that of above θg and a maximum amount of about 30% could be achieved at θ=0°C. Moreover, as reported in [30], isothermal short-time and long-time experiments lead to similar data, meaning that the diffusion of all three small molecules in Estane shows no significant concentration dependency. However, once the θg of the polymer is exceeded, the higher number of molecules is diffused as a result of activation volume according to Eyring’s theory [32], so that after 175 minutes, the sample is totally saturated at θg=80°C. With an increase in temperature, the tortuous route of small penetrants decreases and the system reaches its equilibrium.Figure 3
Simulation results for the temporal development of the changes in concentration of acetone in the middle of Estane samples with rectangular shapes (W × H × L: 2 × 10× 50 mm3) at different temperatures.Another interesting parameter influencing the saturation time of the sample is the geometry as depicted in Figure4. Here, at θ=20°C, the simulation results for temporal changes of acetone concentration in the middle of rectangular and round disk Estane samples have been illustrated for different dimensions. As anticipated, samples with smaller widths are saturated faster than others. Intriguingly, in contrast to the first example, cylindrical specimens with the radius: R=h, are saturated faster than the sample with W=2h.Figure 4
Simulation results of the influence of sample geometry on the amount of sorbed acetone atθ=20°C. Rectangular samples have the dimension: W × H × L: 2 × x × 50 mm3, where x changes from h/4to4h and h is equal to 10 mm. Cylindrical sample is 2 mm thick and has a radius of R=h mm.The results of the diffusion coefficients for the sorption of acetone, ethanol, and water into Estane at three different temperatures are summarized in Table1, respectively. It can be concluded from this table that the diffusivity shows no systematic dependence on the size of probe molecule, as acetone is the biggest and water is the smallest molecule in this study (Figure 5). This is because of the fact that the molecular mobility does not depend on the probe size.Table 1
Diffusion coefficient (D) for sorption of acetone, ethanol, and water into Estane samples at three different temperatures (θ).
Probe molecules
θ (°C)
D×10−14 (m2/s)
Acetone
0
4.217
Acetone
40
13.575
Acetone
80
30.535
Ethanol
0
0.007
Ethanol
40
0.464
Ethanol
80
1.861
Water
0
0.001
Water
40
0.041
Water
80
0.162Figure 5
Structure formula and size of acetone, ethanol, and water, considering a spherical model [33]. The volume of the solvents and their radiuses are calculated from their densities at θ=20°C [34, 35].More important is the correlation between the boiling point of the molecules and their evaporation energies. Molecules with higher boiling points and evaporation energies have smaller diffusion coefficients [35]. Sun and Chen [36] could achieve comparable results about the independence of the size of substituted probe molecules on the sorption and the diffusion processes into polyurethane/polymethyl methacrylate samples.While the diffusivity of acetone at −10°C, that of ethanol at 19°C, and that of water at 91°C are equal, the amount of solvent uptake inside the Estane is different as shown in Figure6. As previously mentioned, here, other parameters like solubility play important roles. Therefore, as can be concluded from the offset of Figure 6, at the beginning, acetone is diffused faster into Estane and then water and finally ethanol. However, after 150 min, ethanol diffuses clearly faster than others and a higher amount could be achieved.Figure 6
Simulation results of the temporal development of the concentration of acetone, ethanol, and water inside the rectangular sample (W × H × L: 2 × 10 × 50 mm3) at θ=−10, 19, and 91°C, respectively.As explained before, the dependency of the diffusion rate and the permeation upon temperature in sorption and desorption processes are evident [37]. To evaluate the activation energy of diffusion, its temperature dependency should be evaluated using the Arrhenius law.
(11)D=D0exp−EaRθ.Here,Ea is the activation energy, θ the absolute temperature, and R the universal gas constant equal to 8.314 J/mol·K.Figure7 shows the plot of lnD versus θ for three studied solvents. As the graph implies, an almost linear dependency can be observed for Estane solvent samples during this temperature range. The values of activation energy for diffusion (E0) can be simply calculated using regression analysis from plots depicted in Figure 7. The apparent activation energies of acetone, ethanol, and water read 32, 58.3, and 56.5 kJ/mol, respectively. These results are in good agreement with activation energies of the same small molecules in similar polyurethanes [30].Figure 7
The temperature dependency of diffusion coefficients of three different solvents (acetone, ethanol, and water) inside Estane to demonstrate the dependence oflnD versus θ for the sorption process. The data are obtained from experimental weight gain measurements.In addition to diffusivity, the cohesive energy density (CED) and Hildebrand’s solubility parameter can be used to calculate the permeability of the sorbents in polymer samples [38]. Hildebrand’s solubility parameter δ=CED is a numerical estimation to indicate the strength of the molecular interaction between solvents and polymers. Materials with the same solubility parameter incline to dissolve in each other. The CED can be understood as the total amount of energy needed to completely remove a unit material volume from its neighbors to infinite separation. This value can be calculated in, for example, MD simulations as an increase in energy per mole material when all intermolecular forces have vanished [20]. The calculated solubility parameters of a representative polyurethane similar to Estane and three solvents are summarized in Table 2. In this contribution, the derivation of cohesive energy density is based on three solubility parameters which have been first introduced by Hildebrand and Scott [38]. Here, it is assumed that the square root of cohesive energy density is a summation of three contributions: dispersion interaction δd, representing the van der Waals type of nonpolar attractive interactions, the δp for interactions between permanent molecular dipoles, and the δh representing a hydrogen type of bonding (H-bonds), which in Hansen’s approach not only addresses interactions related to H-bonds but also integrates other interactions.Table 2
Solubility parameter of Estane, acetone, ethanol, and water as a summation of square Hildebrand and Scott componentsδd, δp, and δh. Data from the handbook of Hansen solubility parameters [38].
Sample
Solubility parameterδ ((MPa)−0.5)
Generic polyurethane
42
Acetone
33
Ethanol
44
Water
73It is clear that the solubility of polyurethane in water is weak and in acetone or ethanol clearly better, indicating that the affinity of polyurethane (Estane) is more toward ethanol or acetone. Moreover, the permeability and solubility parameters are in the same order.Finally, the thermodynamic parameters for diffusion can be calculated using van’t Hoff’s relation [39]:
(12)logKs=ΔS2.303R−ΔH2.303Rθ.Here, (∆H) and (∆S) are the values of change in enthalpy and entropy, respectively, and Ks is the equilibrium sorption constant, which can be estimated from the following equation:
(13)Ks=nseqmp,where nseq denotes the number of moles of the sorbed solvent at the equilibrium. The values of ∆H and ∆S are listed in Table 3. These values were calculated from the slope and intercept of the plot of lnK versus (1/θ). As can be noticed for sorption, the values of ∆H are for all positive sorbents and in the range of 0.0267–0.06 kJ/mol. These positive values of ∆H are an indication for endothermic sorption dominated by the Fickian mode as a result of new pore creation inside the sample.Table 3
Thermodynamic parameters for sorption in Estane and studied solvents.
Thermodynamic parameters
Estane/acetone
Estane/ethanol
Estane/water
∆S (kJ/mol/K)
8.58 × 10−3
4.84 × 10−3
≈0
∆H (kJ/mol)
0.06
0.026
≈0


### 3.2. Determination of Functional Properties of Dry and Hydrolytically Aged Estane

Now that the diffusion of small molecules into polymer matrices has been studied, one can investigate the influence of such low molecular weight compounds on the shape-memory properties of the mentioned polyether urethane samples. As outlined before, in this part, we only concentrate on the effects of physical (hydrolytical) aging on the functional properties of Estane and the influence of other solvents will be discussed in a separate contribution.In order to be able to investigate the influence of physical aging on the functional properties of Estane, theθg of both dry and physically (hydrolytically) aged samples should be first determined and compared.Forθg determination of dry Estane, temperature sweep tests of DMTA experiments were performed. The measured storage shear modulus (G′) and loss shear modulus (G″) for dry Estane are depicted together with the results for physically (hydrolytically) aged samples in Figure 8. As can be observed from this picture, the storage modulus of dry samples starts gradually decreasing with temperature until the temperature reaches the θg of Estane (around 54°C), where because of morphological softening a rapid decrease in the stiffness can be recognized. The G″ on the other hand increases very slightly up to this temperature and sharply decreases from there on with increasing temperature.Figure 8
Comparison of the thermomechanical properties of dry (open symbols) and physically (hydrolytically) aged (solid symbols) Estane obtained from DMTA experiments. Left: changes of storage- (G′) and loss modulus (G″) for dry (open symbols) and physically (hydrolytically) aged samples (solid symbols) in temperature sweep tests. Right: comparison of loss factor tan (ϕ) of dry (open symbols) and (hydrolytically) aged samples (solid symbols) [24].On the other hand, the influence of hydrolytic aging on theθg of Estane is evident. Polymer chains of dry samples are relaxed and in entangled conformation. After physical (hydrolytical) aging, which takes place through diffusion of water molecules, the relaxed polymeric chains are pulled apart from each other and chains experience an internal stress (residual stress) that is counteracted by the tendency of polymer chains to return back to their relaxed minimum energy state.The amount of water uptake for Estane was characterized by mass gain experiments and was found to be around 3 wt.% to 3.1 wt.% at room temperature after one week being settled in a water bath. As can be observed from Figure8, the mechanical properties of physically (hydrolytically) aged samples are different from that of dry ones. This polymer softening (plasticization) effect [40] can be understood as a consequence of a water-induced swelling effect [41] which results in an increase of free volume between polymer chain segments and therefore, in an increase of chain mobility, was approved also by atomistic simulation studies [20, 21]. Moreover, the presented evolution of the loss factor depicted on the right-hand side of Figure 8 reveals that the incorporation of water and consequentially the plasticization effect result in a shift of θg to lower values. From this result, such a shift towards lower θ values with θgwet=48°C becomes obvious. This result could be approved qualitatively by atomistic simulation studies as shown in Figure 9.Figure 9
Results of MD simulations onθg versus the concentration of small molecules, which diffuse into a polymer melt. The polymer melt is modelled here as a coarse-grained linear chain. The small molecules are spherical Lennard-Jones (LJ) particles. Despite the generic feature of the model, the qualitative trend observed here is in agreement with experiments [41]. Results from calculations performed on three independent packing models.It can be observed that theθg decreases with the number density of small particles, diffused into a polymer melt. This trend is in accordance with experimental results shown in Figure 8, where the size of small molecules is smaller than the Kuhn length of the studied polymer. In this figure, θg,0 stands for θg of pure polymers with the same chain length and in the same pressure. The Kunh length is a theoretical concept, which relates the number of conceptual segments in a real polymer chain to the number of segments in an equivalent freely jointed chain model. Since our model chain is chosen to be freely jointed already from the setup, one finds that the Kuhn length is of the order of one bead size (σpp). Therefore, when the size of small particles is smaller than the Kuhn length for polymers, it is observed that increasing the concentration of small particles leads to the reduction of θg in both MD simulations and experimental works.We are aware of the fact that real samples do always contain a distribution of chain lengths and that this may be important for the observed properties. However, in order to gain a first qualitative understanding and for the sake of simplicity, we first focused on a monodisperse system. As mentioned above, despite this simplicity, the model predicts a decrease ofθg upon adding small molecules which is qualitatively in line with experimental results on storage and loss moduli shown in Figure 8, where the temperature corresponding to the maximum of the loss factor is shifted to lower temperatures by adding small molecules (physically (hydrolytically) aged sample). As the next step, it would be indeed very interesting to account for the effect of polydispersity. In view of the computational challenge, we would like to postpone this task to a future work.


### 3.3. Shape-Memory Properties

#### 3.3.1. Shape-Memory Response, Influence of Holding Time

The influence of holding time following the maximum strain ofεm=30% on the SM performance of dry and physically (hydrolytically) aged samples was investigated. Here, dry and physically (hydrolytically) aged specimens have been programmed according to the description mentioned in Section 2.5, which will be explained briefly here. Estane polymer samples were stretched uniaxially at θhigh=70°C during programming from the initially nonstretched extension ε0=0% to the maximum strain of εm=30% and held at this temperature for different holding times in the range of 6–6000 s. Afterwards, the stretched samples were cooled down from θhigh to θlow=10°C, while the stress was kept constant to solidify the oriented polymer chains. After cooling, the samples have been unloaded by releasing the stress and keeping them at θlow, which resulted in temporary fixed strain εu. In the last step, under a stress-free condition, the samples have been brought to θhigh, where the final recovered strains εp are achieved.In Section S3 of Supplement I, Fig.S2 demonstrates the whole SM cycle in two subsequent runs in the stress-temperature-strain (σ-θ-ɛ) diagram for dry Estane stretched up to εm=30%.The evolution of normalized strain with time in recovery modulus for both samples together with the measured shape fixities as a function of time for different holding timesth=6, 60, 600, and 6000 s is depicted in Figure 10. Complementarily, the calculated shape fixities and shape recoveries for the second cycle are listed in Table 4. For comparison reasons, the results for the first cycle are summarized in Table S1 of Section S3 in Supplementary I. A thorough concerned description of results is also included.Figure 10
Development of reduced strains of (a) dry- and (b) physically (hydrolytically) aged Estane samples with 3 wt.% water during the recovery process in the 2nd cycle with different holding times (from 6 to 6000 s) after stretching up toεm=30% at θhigh=70°C in a cyclic thermomechanical tensile test. Achieved shape fixity ratio of (c) dry- and (d) physically (hydrolytically) aged Estane samples with 3 wt.% water after two successive cycles. Results are the average of three similar test runs. The corresponding θ values are plotted as gray lines with respect to the right ordinate.
(a)
Dry Estane
(b)
Hydrolytically aged Estane
(c)
Rf for dry Estane
(d)
Rf for hydrolytically aged EstaneTable 4
Shape-memory properties of dry and physically (hydrolytically) aged Estane programmed atθ=70°C. The results for the first cycle can be found in the Supplement I.
Holding time (s)
Rf (2) (%)
Rr (2) (%)
Dry samples
6
90.71 ± 5.26
65.00 ± 7.01
60
90.11 ± 5.00
60.20 ± 4.14
600
89.84 ± 4.06
43.71 ± 4.23
6000
89.36 ± 4.75
8.00 ± 3.37
Physically (hydrolytically) aged samples
6
91.99 ± 5.79
99.01 ± 5.23
60
92.15 ± 5.97
85.01 ± 3.67
600
90.08 ± 6.78
55.12 ± 4.46
6000
90.16 ± 9.63
33.86 ± 6.12As can be observed from Figures10(a) and 10(b), the reduced strains (ε/εu) for both dry and physically (hydrolytically) aged samples during the recovery processes in the second thermomechanical cycle decrease with a sigmoidal function until it reaches the θg of Estane. For dry samples, the rate of normalized strain began to slow down after 1500 s. By relaxation times larger than 1500 s, a steady normalized strain magnitude (equilibration) has been achieved. Figures 10(a) and 10(b) show that the increase in holding time has two effects on the functional properties of dry and physically (hydrolytically) aged specimens: it resulted in (1) a slower shape recovery rate and (2) a lower shape recovery ratio. Interestingly, obvious higher recovery ratios were obtained for physically (hydrolytically) aged samples. A possible reason for better functional properties of physically (hydrolytically) aged specimen could be presumed in the creation of additional physical crosslinks and different stabilizations of the polymer matrices through H-bond networks, which are created through absorbed water molecules. This shows that even after heating processes during two cycles, the remaining water molecules participate in the recovery procedure and cause an improved shape recovery. The simulation results on SM properties of wet polyesters approve our results [42].At elevated temperatures after deformation, if higher holding time is applied to the material, more time is given to the configurational changes to take place. This means that the material exhibits more resistance against locking in the strain and reasonably lower shape recovery. It was realized that there are chain regions in the molecular network of polymers which are normally inactive in quasistatic deformations but become stretched during fast deformations. The aforementioned regions have loose connectivity to the main load-bearing network and can reach a lower energy state when enough time is given. The relaxation process in polymers involves rapid readjustments of the kinks in local scales and slow rearrangement of the convolutions in long-range scales [43]. One presumption for this observation would be the chain alignment in the polymer matrices with time and consequently the increase in crystalline portions, which needs additional investigations through, for example, wide-angle X-ray scattering (WAXS) experiments [6]. Nevertheless, the number of crystalline portions of unstretched samples could be analyzed by differential scanning calorimetry (DSC) measurements. Such an experiment has been performed for dry Estane, and the results for two successive runs are depicted in Fig. S3 of Section S4 of Supplementary I.The final achieved shape fixity ratios for both dry and physically (hydrolytically) aged samples are depicted in Figures10(c) and 10(d). It can be noticed that the shape fixity ratio of water swollen samples do not contradict with the Rf of the dry specimen between experimental errors. It is believed that at θlow the mobility of chains and water molecules is so limited that no different shape fixation can be observed correspondingly. Moreover, it can be perceived that all samples showed good shape fixation in the range of 89–91%, cf Table 4. Moreover, in the range of experimental errors, shape fixation does not change too much with increasing holding times for both dry and physically (hydrolytically) aged samples. In the literature, one finds different outcomes. While in [44], it was demonstrated that an increase in holding time would improve the shape fixation; exactly the opposite case was reported in [45]. Therefore, it can be concluded that the holding time in stress-controlled experiments may affect the SM properties of the samples totally different [46].


#### 3.3.2. Shape-Memory Response, Influence of Maximum Applied Strain

Another parameter influencing the functional properties and thermomechanical performance of SMPs is the final maximum strains during programming. Therefore, in the next step, dry and physically (hydrolytically) aged samples have been stretched during programming up to different final strainsεm in the range of 10% to 150%. It is noteworthy to mention that the holding time was th=6s for all cycles.Figure11 shows the development of relative strain values of dry and physically (hydrolytically) aged polymer samples during unloading and recovery steps. The calculated shape fixities and shape recoveries of the samples for the second cycle are summarized in Table 5. Again, corresponding supportive results for the first runs can be found in Table S2 of Section S3 of Supplementary I.Figure 11
Development of reduced strain values (ε/εm) for (a) dry- and (b) physically (hydrolytically) aged Estane samples during the unloading process in the 2nd cycle stretched up to different maximum strains εm (from 10% to 150%) at θlow=10°C in a cyclic thermomechanical tensile test. Development of reduced extension values (ε/εu) for (c) dry- and (d) physically (hydrolytically) aged Estane samples during the recovery process in the 2nd cycle stretched up to different maximum strains εm (from 10% to 150%) at θhigh=70°C in a cyclic thermomechanical tensile test.
(a)
Dry Estane
(b)
Hydrolytically aged Estane
(c)
Dry Estane
(d)
Hydrolytically aged EstaneTable 5
Shape-memory properties of dry and physically (hydrolytically) aged Estane programmed atθ=70°C. The results for the first cycle can be found in Supplement I.
Maximum strainεm (−)
Rf (2) (%)
Rr (2) (%)
Dry samples
10%
85.07 ± 3.44
81.02 ± 6.21
30%
91.46 ± 5.75
71.11 ± 6.94
60%
94.47 ± 5.39
69.98 ± 7.34
100%
95.60 ± 6.18
67.18 ± 8.56
150%
95.84 ± 4.28
56.14 ± 6.33
Physically aged samples
10%
93.41 ± 4.25
99.03 ± 3.67
30%
91.99 ± 5.79
95.24 ± 5.23
60%
93.90 ± 5.43
88.20 ± 4.97
100%
94.65 ± 7.63
87.52 ± 6.12
150%
95.60 ± 6.18
84.33 ± 6.18As can be observed from Figures11(a) and 11(b), the different applied maximum strains influenced the shape fixity process of both dry and physically (hydrolytically) aged samples at θlow=10°C. This shows that at θlow polymer samples exhibited elastic response to the applied stretching, but the least part of elongation recovers right after unloading. Although reorientation of polymer chains at this temperature is hard, by increasing final elongations, the amount of unrecoverable strains seems to raise with ɛm.The relative strain valuesε/εm presented in Figures 11(a) and 11(b) can be understood as the development of the apparent shape fixity ratio Rf,app during unloading at θlow=10°C. After a time period of approx. 30 min, the decay in ε/εm is almost completed for dry samples and a plateau value in the range of Rf,app=85%–96% was reached. In comparison, the shape fixation of physically (hydrolytically) aged samples approaches the plateau domain in less time. For physically (hydrolytically) aged Estane, the apparent shape fixity ratio is distinctly higher and in the range of Rf,app=93%–96%. As depicted in Figures 11(a) and 11(b), a rise in εm resulted in an increase of Rf,app from 85% for εm=10% to 96% for εm=150% for dry samples and an increase from 93% for εm=10% to 96% for εm=150% for physically (hydrolytically) aged samples.The development of averaged strain values in relative unitsε/εu for both dry and physically (hydrolytically) aged specimens is illustrated in Figures 11(c) and 11(d). Both dry and physically (hydrolytically) aged Estane showed qualitatively similar recovery behavior, whereby a plateau value could be attained for times larger than t>30 min. For the recovery step, the normalized representation of ε/εu as a function of time shows an obvious dependency on the maximum strains (cf Table 5). It can be revealed that with increasing maximum strains εm, the shape recoverability Rr of both samples decreased from 81% to 56% for dry and from 99% to 84% in the case of physically (hydrolytically) aged samples.It can be observed that the shape recovery effect decreases because of an increase in the amount of nonrecoverable (plastic) parts of the shape changes with an increase inεm. This could be a consequence of oriented crystalline structures [47–49]. The observed decrease in recovery effects with an increasing final maximum strain has also been reported for other SMPs [50, 51].Maximum final elongations do not only affect the shape recovery values but also influence the shape recovery rate of the samples. In Figure12, the development of reduced strain values ε/εu for dry Estane in the recovery step is depicted as a function of temperature in the range of 55–65°C. As can be indicated from Figure 12, the lower the strains ε are, the faster is the recovery around θg. This finding might be interesting for applications, where faster recovery is demanded.Figure 12
Development of reducedε values for dry Estane during the recovery process in the 2nd cycle stretched up to different maximum strains εm (from 10% to 150%) at θhigh=70°C in a cyclic thermomechanical tensile test.


## 3.1. Diffusion Behavior of Small Molecules into Estane Samples

The Fickian conduct of acetone, ethanol, and water inside Estane is studied at different temperatures experimentally and by the mean of finite element simulations. Since the qualitative behavior of the diffusion processes of the mentioned solvents into Estane is similar, only the results for acetone are shown here.The simulation results for the temporal evolution of the concentration of acetone in the middle of the sample (W × H × L: 2 × 10 × 50 mm3) for different temperatures modeled are shown in Figure 3. As can be recognized from this picture, the amount of acetone molecules which are diffused inside the sample, increases with temperature and the concentration profile has a biphasic form. Below θg, the increase of acetone concentration is clearly lower than that of above θg and a maximum amount of about 30% could be achieved at θ=0°C. Moreover, as reported in [30], isothermal short-time and long-time experiments lead to similar data, meaning that the diffusion of all three small molecules in Estane shows no significant concentration dependency. However, once the θg of the polymer is exceeded, the higher number of molecules is diffused as a result of activation volume according to Eyring’s theory [32], so that after 175 minutes, the sample is totally saturated at θg=80°C. With an increase in temperature, the tortuous route of small penetrants decreases and the system reaches its equilibrium.Figure 3
Simulation results for the temporal development of the changes in concentration of acetone in the middle of Estane samples with rectangular shapes (W × H × L: 2 × 10× 50 mm3) at different temperatures.Another interesting parameter influencing the saturation time of the sample is the geometry as depicted in Figure4. Here, at θ=20°C, the simulation results for temporal changes of acetone concentration in the middle of rectangular and round disk Estane samples have been illustrated for different dimensions. As anticipated, samples with smaller widths are saturated faster than others. Intriguingly, in contrast to the first example, cylindrical specimens with the radius: R=h, are saturated faster than the sample with W=2h.Figure 4
Simulation results of the influence of sample geometry on the amount of sorbed acetone atθ=20°C. Rectangular samples have the dimension: W × H × L: 2 × x × 50 mm3, where x changes from h/4to4h and h is equal to 10 mm. Cylindrical sample is 2 mm thick and has a radius of R=h mm.The results of the diffusion coefficients for the sorption of acetone, ethanol, and water into Estane at three different temperatures are summarized in Table1, respectively. It can be concluded from this table that the diffusivity shows no systematic dependence on the size of probe molecule, as acetone is the biggest and water is the smallest molecule in this study (Figure 5). This is because of the fact that the molecular mobility does not depend on the probe size.Table 1
Diffusion coefficient (D) for sorption of acetone, ethanol, and water into Estane samples at three different temperatures (θ).
Probe molecules
θ (°C)
D×10−14 (m2/s)
Acetone
0
4.217
Acetone
40
13.575
Acetone
80
30.535
Ethanol
0
0.007
Ethanol
40
0.464
Ethanol
80
1.861
Water
0
0.001
Water
40
0.041
Water
80
0.162Figure 5
Structure formula and size of acetone, ethanol, and water, considering a spherical model [33]. The volume of the solvents and their radiuses are calculated from their densities at θ=20°C [34, 35].More important is the correlation between the boiling point of the molecules and their evaporation energies. Molecules with higher boiling points and evaporation energies have smaller diffusion coefficients [35]. Sun and Chen [36] could achieve comparable results about the independence of the size of substituted probe molecules on the sorption and the diffusion processes into polyurethane/polymethyl methacrylate samples.While the diffusivity of acetone at −10°C, that of ethanol at 19°C, and that of water at 91°C are equal, the amount of solvent uptake inside the Estane is different as shown in Figure6. As previously mentioned, here, other parameters like solubility play important roles. Therefore, as can be concluded from the offset of Figure 6, at the beginning, acetone is diffused faster into Estane and then water and finally ethanol. However, after 150 min, ethanol diffuses clearly faster than others and a higher amount could be achieved.Figure 6
Simulation results of the temporal development of the concentration of acetone, ethanol, and water inside the rectangular sample (W × H × L: 2 × 10 × 50 mm3) at θ=−10, 19, and 91°C, respectively.As explained before, the dependency of the diffusion rate and the permeation upon temperature in sorption and desorption processes are evident [37]. To evaluate the activation energy of diffusion, its temperature dependency should be evaluated using the Arrhenius law.
(11)D=D0exp−EaRθ.Here,Ea is the activation energy, θ the absolute temperature, and R the universal gas constant equal to 8.314 J/mol·K.Figure7 shows the plot of lnD versus θ for three studied solvents. As the graph implies, an almost linear dependency can be observed for Estane solvent samples during this temperature range. The values of activation energy for diffusion (E0) can be simply calculated using regression analysis from plots depicted in Figure 7. The apparent activation energies of acetone, ethanol, and water read 32, 58.3, and 56.5 kJ/mol, respectively. These results are in good agreement with activation energies of the same small molecules in similar polyurethanes [30].Figure 7
The temperature dependency of diffusion coefficients of three different solvents (acetone, ethanol, and water) inside Estane to demonstrate the dependence oflnD versus θ for the sorption process. The data are obtained from experimental weight gain measurements.In addition to diffusivity, the cohesive energy density (CED) and Hildebrand’s solubility parameter can be used to calculate the permeability of the sorbents in polymer samples [38]. Hildebrand’s solubility parameter δ=CED is a numerical estimation to indicate the strength of the molecular interaction between solvents and polymers. Materials with the same solubility parameter incline to dissolve in each other. The CED can be understood as the total amount of energy needed to completely remove a unit material volume from its neighbors to infinite separation. This value can be calculated in, for example, MD simulations as an increase in energy per mole material when all intermolecular forces have vanished [20]. The calculated solubility parameters of a representative polyurethane similar to Estane and three solvents are summarized in Table 2. In this contribution, the derivation of cohesive energy density is based on three solubility parameters which have been first introduced by Hildebrand and Scott [38]. Here, it is assumed that the square root of cohesive energy density is a summation of three contributions: dispersion interaction δd, representing the van der Waals type of nonpolar attractive interactions, the δp for interactions between permanent molecular dipoles, and the δh representing a hydrogen type of bonding (H-bonds), which in Hansen’s approach not only addresses interactions related to H-bonds but also integrates other interactions.Table 2
Solubility parameter of Estane, acetone, ethanol, and water as a summation of square Hildebrand and Scott componentsδd, δp, and δh. Data from the handbook of Hansen solubility parameters [38].
Sample
Solubility parameterδ ((MPa)−0.5)
Generic polyurethane
42
Acetone
33
Ethanol
44
Water
73It is clear that the solubility of polyurethane in water is weak and in acetone or ethanol clearly better, indicating that the affinity of polyurethane (Estane) is more toward ethanol or acetone. Moreover, the permeability and solubility parameters are in the same order.Finally, the thermodynamic parameters for diffusion can be calculated using van’t Hoff’s relation [39]:
(12)logKs=ΔS2.303R−ΔH2.303Rθ.Here, (∆H) and (∆S) are the values of change in enthalpy and entropy, respectively, and Ks is the equilibrium sorption constant, which can be estimated from the following equation:
(13)Ks=nseqmp,where nseq denotes the number of moles of the sorbed solvent at the equilibrium. The values of ∆H and ∆S are listed in Table 3. These values were calculated from the slope and intercept of the plot of lnK versus (1/θ). As can be noticed for sorption, the values of ∆H are for all positive sorbents and in the range of 0.0267–0.06 kJ/mol. These positive values of ∆H are an indication for endothermic sorption dominated by the Fickian mode as a result of new pore creation inside the sample.Table 3
Thermodynamic parameters for sorption in Estane and studied solvents.
Thermodynamic parameters
Estane/acetone
Estane/ethanol
Estane/water
∆S (kJ/mol/K)
8.58 × 10−3
4.84 × 10−3
≈0
∆H (kJ/mol)
0.06
0.026
≈0


## 3.2. Determination of Functional Properties of Dry and Hydrolytically Aged Estane

Now that the diffusion of small molecules into polymer matrices has been studied, one can investigate the influence of such low molecular weight compounds on the shape-memory properties of the mentioned polyether urethane samples. As outlined before, in this part, we only concentrate on the effects of physical (hydrolytical) aging on the functional properties of Estane and the influence of other solvents will be discussed in a separate contribution.In order to be able to investigate the influence of physical aging on the functional properties of Estane, theθg of both dry and physically (hydrolytically) aged samples should be first determined and compared.Forθg determination of dry Estane, temperature sweep tests of DMTA experiments were performed. The measured storage shear modulus (G′) and loss shear modulus (G″) for dry Estane are depicted together with the results for physically (hydrolytically) aged samples in Figure 8. As can be observed from this picture, the storage modulus of dry samples starts gradually decreasing with temperature until the temperature reaches the θg of Estane (around 54°C), where because of morphological softening a rapid decrease in the stiffness can be recognized. The G″ on the other hand increases very slightly up to this temperature and sharply decreases from there on with increasing temperature.Figure 8
Comparison of the thermomechanical properties of dry (open symbols) and physically (hydrolytically) aged (solid symbols) Estane obtained from DMTA experiments. Left: changes of storage- (G′) and loss modulus (G″) for dry (open symbols) and physically (hydrolytically) aged samples (solid symbols) in temperature sweep tests. Right: comparison of loss factor tan (ϕ) of dry (open symbols) and (hydrolytically) aged samples (solid symbols) [24].On the other hand, the influence of hydrolytic aging on theθg of Estane is evident. Polymer chains of dry samples are relaxed and in entangled conformation. After physical (hydrolytical) aging, which takes place through diffusion of water molecules, the relaxed polymeric chains are pulled apart from each other and chains experience an internal stress (residual stress) that is counteracted by the tendency of polymer chains to return back to their relaxed minimum energy state.The amount of water uptake for Estane was characterized by mass gain experiments and was found to be around 3 wt.% to 3.1 wt.% at room temperature after one week being settled in a water bath. As can be observed from Figure8, the mechanical properties of physically (hydrolytically) aged samples are different from that of dry ones. This polymer softening (plasticization) effect [40] can be understood as a consequence of a water-induced swelling effect [41] which results in an increase of free volume between polymer chain segments and therefore, in an increase of chain mobility, was approved also by atomistic simulation studies [20, 21]. Moreover, the presented evolution of the loss factor depicted on the right-hand side of Figure 8 reveals that the incorporation of water and consequentially the plasticization effect result in a shift of θg to lower values. From this result, such a shift towards lower θ values with θgwet=48°C becomes obvious. This result could be approved qualitatively by atomistic simulation studies as shown in Figure 9.Figure 9
Results of MD simulations onθg versus the concentration of small molecules, which diffuse into a polymer melt. The polymer melt is modelled here as a coarse-grained linear chain. The small molecules are spherical Lennard-Jones (LJ) particles. Despite the generic feature of the model, the qualitative trend observed here is in agreement with experiments [41]. Results from calculations performed on three independent packing models.It can be observed that theθg decreases with the number density of small particles, diffused into a polymer melt. This trend is in accordance with experimental results shown in Figure 8, where the size of small molecules is smaller than the Kuhn length of the studied polymer. In this figure, θg,0 stands for θg of pure polymers with the same chain length and in the same pressure. The Kunh length is a theoretical concept, which relates the number of conceptual segments in a real polymer chain to the number of segments in an equivalent freely jointed chain model. Since our model chain is chosen to be freely jointed already from the setup, one finds that the Kuhn length is of the order of one bead size (σpp). Therefore, when the size of small particles is smaller than the Kuhn length for polymers, it is observed that increasing the concentration of small particles leads to the reduction of θg in both MD simulations and experimental works.We are aware of the fact that real samples do always contain a distribution of chain lengths and that this may be important for the observed properties. However, in order to gain a first qualitative understanding and for the sake of simplicity, we first focused on a monodisperse system. As mentioned above, despite this simplicity, the model predicts a decrease ofθg upon adding small molecules which is qualitatively in line with experimental results on storage and loss moduli shown in Figure 8, where the temperature corresponding to the maximum of the loss factor is shifted to lower temperatures by adding small molecules (physically (hydrolytically) aged sample). As the next step, it would be indeed very interesting to account for the effect of polydispersity. In view of the computational challenge, we would like to postpone this task to a future work.


## 3.3. Shape-Memory Properties

### 3.3.1. Shape-Memory Response, Influence of Holding Time

The influence of holding time following the maximum strain ofεm=30% on the SM performance of dry and physically (hydrolytically) aged samples was investigated. Here, dry and physically (hydrolytically) aged specimens have been programmed according to the description mentioned in Section 2.5, which will be explained briefly here. Estane polymer samples were stretched uniaxially at θhigh=70°C during programming from the initially nonstretched extension ε0=0% to the maximum strain of εm=30% and held at this temperature for different holding times in the range of 6–6000 s. Afterwards, the stretched samples were cooled down from θhigh to θlow=10°C, while the stress was kept constant to solidify the oriented polymer chains. After cooling, the samples have been unloaded by releasing the stress and keeping them at θlow, which resulted in temporary fixed strain εu. In the last step, under a stress-free condition, the samples have been brought to θhigh, where the final recovered strains εp are achieved.In Section S3 of Supplement I, Fig.S2 demonstrates the whole SM cycle in two subsequent runs in the stress-temperature-strain (σ-θ-ɛ) diagram for dry Estane stretched up to εm=30%.The evolution of normalized strain with time in recovery modulus for both samples together with the measured shape fixities as a function of time for different holding timesth=6, 60, 600, and 6000 s is depicted in Figure 10. Complementarily, the calculated shape fixities and shape recoveries for the second cycle are listed in Table 4. For comparison reasons, the results for the first cycle are summarized in Table S1 of Section S3 in Supplementary I. A thorough concerned description of results is also included.Figure 10
Development of reduced strains of (a) dry- and (b) physically (hydrolytically) aged Estane samples with 3 wt.% water during the recovery process in the 2nd cycle with different holding times (from 6 to 6000 s) after stretching up toεm=30% at θhigh=70°C in a cyclic thermomechanical tensile test. Achieved shape fixity ratio of (c) dry- and (d) physically (hydrolytically) aged Estane samples with 3 wt.% water after two successive cycles. Results are the average of three similar test runs. The corresponding θ values are plotted as gray lines with respect to the right ordinate.
(a)
Dry Estane
(b)
Hydrolytically aged Estane
(c)
Rf for dry Estane
(d)
Rf for hydrolytically aged EstaneTable 4
Shape-memory properties of dry and physically (hydrolytically) aged Estane programmed atθ=70°C. The results for the first cycle can be found in the Supplement I.
Holding time (s)
Rf (2) (%)
Rr (2) (%)
Dry samples
6
90.71 ± 5.26
65.00 ± 7.01
60
90.11 ± 5.00
60.20 ± 4.14
600
89.84 ± 4.06
43.71 ± 4.23
6000
89.36 ± 4.75
8.00 ± 3.37
Physically (hydrolytically) aged samples
6
91.99 ± 5.79
99.01 ± 5.23
60
92.15 ± 5.97
85.01 ± 3.67
600
90.08 ± 6.78
55.12 ± 4.46
6000
90.16 ± 9.63
33.86 ± 6.12As can be observed from Figures10(a) and 10(b), the reduced strains (ε/εu) for both dry and physically (hydrolytically) aged samples during the recovery processes in the second thermomechanical cycle decrease with a sigmoidal function until it reaches the θg of Estane. For dry samples, the rate of normalized strain began to slow down after 1500 s. By relaxation times larger than 1500 s, a steady normalized strain magnitude (equilibration) has been achieved. Figures 10(a) and 10(b) show that the increase in holding time has two effects on the functional properties of dry and physically (hydrolytically) aged specimens: it resulted in (1) a slower shape recovery rate and (2) a lower shape recovery ratio. Interestingly, obvious higher recovery ratios were obtained for physically (hydrolytically) aged samples. A possible reason for better functional properties of physically (hydrolytically) aged specimen could be presumed in the creation of additional physical crosslinks and different stabilizations of the polymer matrices through H-bond networks, which are created through absorbed water molecules. This shows that even after heating processes during two cycles, the remaining water molecules participate in the recovery procedure and cause an improved shape recovery. The simulation results on SM properties of wet polyesters approve our results [42].At elevated temperatures after deformation, if higher holding time is applied to the material, more time is given to the configurational changes to take place. This means that the material exhibits more resistance against locking in the strain and reasonably lower shape recovery. It was realized that there are chain regions in the molecular network of polymers which are normally inactive in quasistatic deformations but become stretched during fast deformations. The aforementioned regions have loose connectivity to the main load-bearing network and can reach a lower energy state when enough time is given. The relaxation process in polymers involves rapid readjustments of the kinks in local scales and slow rearrangement of the convolutions in long-range scales [43]. One presumption for this observation would be the chain alignment in the polymer matrices with time and consequently the increase in crystalline portions, which needs additional investigations through, for example, wide-angle X-ray scattering (WAXS) experiments [6]. Nevertheless, the number of crystalline portions of unstretched samples could be analyzed by differential scanning calorimetry (DSC) measurements. Such an experiment has been performed for dry Estane, and the results for two successive runs are depicted in Fig. S3 of Section S4 of Supplementary I.The final achieved shape fixity ratios for both dry and physically (hydrolytically) aged samples are depicted in Figures10(c) and 10(d). It can be noticed that the shape fixity ratio of water swollen samples do not contradict with the Rf of the dry specimen between experimental errors. It is believed that at θlow the mobility of chains and water molecules is so limited that no different shape fixation can be observed correspondingly. Moreover, it can be perceived that all samples showed good shape fixation in the range of 89–91%, cf Table 4. Moreover, in the range of experimental errors, shape fixation does not change too much with increasing holding times for both dry and physically (hydrolytically) aged samples. In the literature, one finds different outcomes. While in [44], it was demonstrated that an increase in holding time would improve the shape fixation; exactly the opposite case was reported in [45]. Therefore, it can be concluded that the holding time in stress-controlled experiments may affect the SM properties of the samples totally different [46].


### 3.3.2. Shape-Memory Response, Influence of Maximum Applied Strain

Another parameter influencing the functional properties and thermomechanical performance of SMPs is the final maximum strains during programming. Therefore, in the next step, dry and physically (hydrolytically) aged samples have been stretched during programming up to different final strainsεm in the range of 10% to 150%. It is noteworthy to mention that the holding time was th=6s for all cycles.Figure11 shows the development of relative strain values of dry and physically (hydrolytically) aged polymer samples during unloading and recovery steps. The calculated shape fixities and shape recoveries of the samples for the second cycle are summarized in Table 5. Again, corresponding supportive results for the first runs can be found in Table S2 of Section S3 of Supplementary I.Figure 11
Development of reduced strain values (ε/εm) for (a) dry- and (b) physically (hydrolytically) aged Estane samples during the unloading process in the 2nd cycle stretched up to different maximum strains εm (from 10% to 150%) at θlow=10°C in a cyclic thermomechanical tensile test. Development of reduced extension values (ε/εu) for (c) dry- and (d) physically (hydrolytically) aged Estane samples during the recovery process in the 2nd cycle stretched up to different maximum strains εm (from 10% to 150%) at θhigh=70°C in a cyclic thermomechanical tensile test.
(a)
Dry Estane
(b)
Hydrolytically aged Estane
(c)
Dry Estane
(d)
Hydrolytically aged EstaneTable 5
Shape-memory properties of dry and physically (hydrolytically) aged Estane programmed atθ=70°C. The results for the first cycle can be found in Supplement I.
Maximum strainεm (−)
Rf (2) (%)
Rr (2) (%)
Dry samples
10%
85.07 ± 3.44
81.02 ± 6.21
30%
91.46 ± 5.75
71.11 ± 6.94
60%
94.47 ± 5.39
69.98 ± 7.34
100%
95.60 ± 6.18
67.18 ± 8.56
150%
95.84 ± 4.28
56.14 ± 6.33
Physically aged samples
10%
93.41 ± 4.25
99.03 ± 3.67
30%
91.99 ± 5.79
95.24 ± 5.23
60%
93.90 ± 5.43
88.20 ± 4.97
100%
94.65 ± 7.63
87.52 ± 6.12
150%
95.60 ± 6.18
84.33 ± 6.18As can be observed from Figures11(a) and 11(b), the different applied maximum strains influenced the shape fixity process of both dry and physically (hydrolytically) aged samples at θlow=10°C. This shows that at θlow polymer samples exhibited elastic response to the applied stretching, but the least part of elongation recovers right after unloading. Although reorientation of polymer chains at this temperature is hard, by increasing final elongations, the amount of unrecoverable strains seems to raise with ɛm.The relative strain valuesε/εm presented in Figures 11(a) and 11(b) can be understood as the development of the apparent shape fixity ratio Rf,app during unloading at θlow=10°C. After a time period of approx. 30 min, the decay in ε/εm is almost completed for dry samples and a plateau value in the range of Rf,app=85%–96% was reached. In comparison, the shape fixation of physically (hydrolytically) aged samples approaches the plateau domain in less time. For physically (hydrolytically) aged Estane, the apparent shape fixity ratio is distinctly higher and in the range of Rf,app=93%–96%. As depicted in Figures 11(a) and 11(b), a rise in εm resulted in an increase of Rf,app from 85% for εm=10% to 96% for εm=150% for dry samples and an increase from 93% for εm=10% to 96% for εm=150% for physically (hydrolytically) aged samples.The development of averaged strain values in relative unitsε/εu for both dry and physically (hydrolytically) aged specimens is illustrated in Figures 11(c) and 11(d). Both dry and physically (hydrolytically) aged Estane showed qualitatively similar recovery behavior, whereby a plateau value could be attained for times larger than t>30 min. For the recovery step, the normalized representation of ε/εu as a function of time shows an obvious dependency on the maximum strains (cf Table 5). It can be revealed that with increasing maximum strains εm, the shape recoverability Rr of both samples decreased from 81% to 56% for dry and from 99% to 84% in the case of physically (hydrolytically) aged samples.It can be observed that the shape recovery effect decreases because of an increase in the amount of nonrecoverable (plastic) parts of the shape changes with an increase inεm. This could be a consequence of oriented crystalline structures [47–49]. The observed decrease in recovery effects with an increasing final maximum strain has also been reported for other SMPs [50, 51].Maximum final elongations do not only affect the shape recovery values but also influence the shape recovery rate of the samples. In Figure12, the development of reduced strain values ε/εu for dry Estane in the recovery step is depicted as a function of temperature in the range of 55–65°C. As can be indicated from Figure 12, the lower the strains ε are, the faster is the recovery around θg. This finding might be interesting for applications, where faster recovery is demanded.Figure 12
Development of reducedε values for dry Estane during the recovery process in the 2nd cycle stretched up to different maximum strains εm (from 10% to 150%) at θhigh=70°C in a cyclic thermomechanical tensile test.


## 3.3.1. Shape-Memory Response, Influence of Holding Time

The influence of holding time following the maximum strain ofεm=30% on the SM performance of dry and physically (hydrolytically) aged samples was investigated. Here, dry and physically (hydrolytically) aged specimens have been programmed according to the description mentioned in Section 2.5, which will be explained briefly here. Estane polymer samples were stretched uniaxially at θhigh=70°C during programming from the initially nonstretched extension ε0=0% to the maximum strain of εm=30% and held at this temperature for different holding times in the range of 6–6000 s. Afterwards, the stretched samples were cooled down from θhigh to θlow=10°C, while the stress was kept constant to solidify the oriented polymer chains. After cooling, the samples have been unloaded by releasing the stress and keeping them at θlow, which resulted in temporary fixed strain εu. In the last step, under a stress-free condition, the samples have been brought to θhigh, where the final recovered strains εp are achieved.In Section S3 of Supplement I, Fig.S2 demonstrates the whole SM cycle in two subsequent runs in the stress-temperature-strain (σ-θ-ɛ) diagram for dry Estane stretched up to εm=30%.The evolution of normalized strain with time in recovery modulus for both samples together with the measured shape fixities as a function of time for different holding timesth=6, 60, 600, and 6000 s is depicted in Figure 10. Complementarily, the calculated shape fixities and shape recoveries for the second cycle are listed in Table 4. For comparison reasons, the results for the first cycle are summarized in Table S1 of Section S3 in Supplementary I. A thorough concerned description of results is also included.Figure 10
Development of reduced strains of (a) dry- and (b) physically (hydrolytically) aged Estane samples with 3 wt.% water during the recovery process in the 2nd cycle with different holding times (from 6 to 6000 s) after stretching up toεm=30% at θhigh=70°C in a cyclic thermomechanical tensile test. Achieved shape fixity ratio of (c) dry- and (d) physically (hydrolytically) aged Estane samples with 3 wt.% water after two successive cycles. Results are the average of three similar test runs. The corresponding θ values are plotted as gray lines with respect to the right ordinate.
(a)
Dry Estane
(b)
Hydrolytically aged Estane
(c)
Rf for dry Estane
(d)
Rf for hydrolytically aged EstaneTable 4
Shape-memory properties of dry and physically (hydrolytically) aged Estane programmed atθ=70°C. The results for the first cycle can be found in the Supplement I.
Holding time (s)
Rf (2) (%)
Rr (2) (%)
Dry samples
6
90.71 ± 5.26
65.00 ± 7.01
60
90.11 ± 5.00
60.20 ± 4.14
600
89.84 ± 4.06
43.71 ± 4.23
6000
89.36 ± 4.75
8.00 ± 3.37
Physically (hydrolytically) aged samples
6
91.99 ± 5.79
99.01 ± 5.23
60
92.15 ± 5.97
85.01 ± 3.67
600
90.08 ± 6.78
55.12 ± 4.46
6000
90.16 ± 9.63
33.86 ± 6.12As can be observed from Figures10(a) and 10(b), the reduced strains (ε/εu) for both dry and physically (hydrolytically) aged samples during the recovery processes in the second thermomechanical cycle decrease with a sigmoidal function until it reaches the θg of Estane. For dry samples, the rate of normalized strain began to slow down after 1500 s. By relaxation times larger than 1500 s, a steady normalized strain magnitude (equilibration) has been achieved. Figures 10(a) and 10(b) show that the increase in holding time has two effects on the functional properties of dry and physically (hydrolytically) aged specimens: it resulted in (1) a slower shape recovery rate and (2) a lower shape recovery ratio. Interestingly, obvious higher recovery ratios were obtained for physically (hydrolytically) aged samples. A possible reason for better functional properties of physically (hydrolytically) aged specimen could be presumed in the creation of additional physical crosslinks and different stabilizations of the polymer matrices through H-bond networks, which are created through absorbed water molecules. This shows that even after heating processes during two cycles, the remaining water molecules participate in the recovery procedure and cause an improved shape recovery. The simulation results on SM properties of wet polyesters approve our results [42].At elevated temperatures after deformation, if higher holding time is applied to the material, more time is given to the configurational changes to take place. This means that the material exhibits more resistance against locking in the strain and reasonably lower shape recovery. It was realized that there are chain regions in the molecular network of polymers which are normally inactive in quasistatic deformations but become stretched during fast deformations. The aforementioned regions have loose connectivity to the main load-bearing network and can reach a lower energy state when enough time is given. The relaxation process in polymers involves rapid readjustments of the kinks in local scales and slow rearrangement of the convolutions in long-range scales [43]. One presumption for this observation would be the chain alignment in the polymer matrices with time and consequently the increase in crystalline portions, which needs additional investigations through, for example, wide-angle X-ray scattering (WAXS) experiments [6]. Nevertheless, the number of crystalline portions of unstretched samples could be analyzed by differential scanning calorimetry (DSC) measurements. Such an experiment has been performed for dry Estane, and the results for two successive runs are depicted in Fig. S3 of Section S4 of Supplementary I.The final achieved shape fixity ratios for both dry and physically (hydrolytically) aged samples are depicted in Figures10(c) and 10(d). It can be noticed that the shape fixity ratio of water swollen samples do not contradict with the Rf of the dry specimen between experimental errors. It is believed that at θlow the mobility of chains and water molecules is so limited that no different shape fixation can be observed correspondingly. Moreover, it can be perceived that all samples showed good shape fixation in the range of 89–91%, cf Table 4. Moreover, in the range of experimental errors, shape fixation does not change too much with increasing holding times for both dry and physically (hydrolytically) aged samples. In the literature, one finds different outcomes. While in [44], it was demonstrated that an increase in holding time would improve the shape fixation; exactly the opposite case was reported in [45]. Therefore, it can be concluded that the holding time in stress-controlled experiments may affect the SM properties of the samples totally different [46].


## 3.3.2. Shape-Memory Response, Influence of Maximum Applied Strain

Another parameter influencing the functional properties and thermomechanical performance of SMPs is the final maximum strains during programming. Therefore, in the next step, dry and physically (hydrolytically) aged samples have been stretched during programming up to different final strainsεm in the range of 10% to 150%. It is noteworthy to mention that the holding time was th=6s for all cycles.Figure11 shows the development of relative strain values of dry and physically (hydrolytically) aged polymer samples during unloading and recovery steps. The calculated shape fixities and shape recoveries of the samples for the second cycle are summarized in Table 5. Again, corresponding supportive results for the first runs can be found in Table S2 of Section S3 of Supplementary I.Figure 11
Development of reduced strain values (ε/εm) for (a) dry- and (b) physically (hydrolytically) aged Estane samples during the unloading process in the 2nd cycle stretched up to different maximum strains εm (from 10% to 150%) at θlow=10°C in a cyclic thermomechanical tensile test. Development of reduced extension values (ε/εu) for (c) dry- and (d) physically (hydrolytically) aged Estane samples during the recovery process in the 2nd cycle stretched up to different maximum strains εm (from 10% to 150%) at θhigh=70°C in a cyclic thermomechanical tensile test.
(a)
Dry Estane
(b)
Hydrolytically aged Estane
(c)
Dry Estane
(d)
Hydrolytically aged EstaneTable 5
Shape-memory properties of dry and physically (hydrolytically) aged Estane programmed atθ=70°C. The results for the first cycle can be found in Supplement I.
Maximum strainεm (−)
Rf (2) (%)
Rr (2) (%)
Dry samples
10%
85.07 ± 3.44
81.02 ± 6.21
30%
91.46 ± 5.75
71.11 ± 6.94
60%
94.47 ± 5.39
69.98 ± 7.34
100%
95.60 ± 6.18
67.18 ± 8.56
150%
95.84 ± 4.28
56.14 ± 6.33
Physically aged samples
10%
93.41 ± 4.25
99.03 ± 3.67
30%
91.99 ± 5.79
95.24 ± 5.23
60%
93.90 ± 5.43
88.20 ± 4.97
100%
94.65 ± 7.63
87.52 ± 6.12
150%
95.60 ± 6.18
84.33 ± 6.18As can be observed from Figures11(a) and 11(b), the different applied maximum strains influenced the shape fixity process of both dry and physically (hydrolytically) aged samples at θlow=10°C. This shows that at θlow polymer samples exhibited elastic response to the applied stretching, but the least part of elongation recovers right after unloading. Although reorientation of polymer chains at this temperature is hard, by increasing final elongations, the amount of unrecoverable strains seems to raise with ɛm.The relative strain valuesε/εm presented in Figures 11(a) and 11(b) can be understood as the development of the apparent shape fixity ratio Rf,app during unloading at θlow=10°C. After a time period of approx. 30 min, the decay in ε/εm is almost completed for dry samples and a plateau value in the range of Rf,app=85%–96% was reached. In comparison, the shape fixation of physically (hydrolytically) aged samples approaches the plateau domain in less time. For physically (hydrolytically) aged Estane, the apparent shape fixity ratio is distinctly higher and in the range of Rf,app=93%–96%. As depicted in Figures 11(a) and 11(b), a rise in εm resulted in an increase of Rf,app from 85% for εm=10% to 96% for εm=150% for dry samples and an increase from 93% for εm=10% to 96% for εm=150% for physically (hydrolytically) aged samples.The development of averaged strain values in relative unitsε/εu for both dry and physically (hydrolytically) aged specimens is illustrated in Figures 11(c) and 11(d). Both dry and physically (hydrolytically) aged Estane showed qualitatively similar recovery behavior, whereby a plateau value could be attained for times larger than t>30 min. For the recovery step, the normalized representation of ε/εu as a function of time shows an obvious dependency on the maximum strains (cf Table 5). It can be revealed that with increasing maximum strains εm, the shape recoverability Rr of both samples decreased from 81% to 56% for dry and from 99% to 84% in the case of physically (hydrolytically) aged samples.It can be observed that the shape recovery effect decreases because of an increase in the amount of nonrecoverable (plastic) parts of the shape changes with an increase inεm. This could be a consequence of oriented crystalline structures [47–49]. The observed decrease in recovery effects with an increasing final maximum strain has also been reported for other SMPs [50, 51].Maximum final elongations do not only affect the shape recovery values but also influence the shape recovery rate of the samples. In Figure12, the development of reduced strain values ε/εu for dry Estane in the recovery step is depicted as a function of temperature in the range of 55–65°C. As can be indicated from Figure 12, the lower the strains ε are, the faster is the recovery around θg. This finding might be interesting for applications, where faster recovery is demanded.Figure 12
Development of reducedε values for dry Estane during the recovery process in the 2nd cycle stretched up to different maximum strains εm (from 10% to 150%) at θhigh=70°C in a cyclic thermomechanical tensile test.


## 4. Conclusion

In the present contribution, we first studied the transport behavior of three substituted compounds (acetone, ethanol, and water) through Estane experimentally and with numerical simulations. It was revealed that even after 1 week, putting the samples in the corresponding solvent bathes, neither enthalpy relaxation nor monomer release, could occur because of the lack of hydrophilic groups. Moreover, it was demonstrated that theθg lowering of physically aged samples was due to the plasticization effects and a consequence of higher capability of low molecular weight compounds and oriented polymer chains for molecular movements in a low energetic state. The increase in the interaction of water molecules with polar chain groups leads to disrupting the weak molecular interactions of adjacent polymer chains. This could be approved by atomistic simulation studies that indicated a θg-lowering of freely jointed polymer systems up to 7% for 12% number concentrations of spherical Lennard-Jones (LJ) particles.Moreover, the influence of physical (hydrolytical) aging, through the incorporation of 3 wt.% water molecules into dry polymer matrices on the functional properties of the Estane, was studied. Dry and physically (hydrolytically) aged samples have been conducted to different maximum strains and different holding times. It could be indicated that the shape fixation of physically (hydrolytically) aged polymers do not differ from dry samples in the range of statistical errors. However, physical (hydrolytic) aging resulted in an obvious better and faster shape recovery ratio as a result of additional physical crosslinks.We assume that the presented findings might motivate further knowledge-based researches for designing polymer systems with defined SM parameters.



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*Source: 7819353-2018-05-28.xml*