Authors: Suellen Pereira Espíndola, Ben Norder, Ger J. M. Koper, Stephen J. Picken
Categories: Article
Source: Biomacromolecules
Temperature of Heterogeneous Biopolymer Systems
Biopolymers are abundant, renewable, and biodegradable
resources.
However, bio-based materials often require toughening additives, like
(co)polymers or small plasticizing molecules. Plasticization is monitored
via the glass transition temperature versus diluent content. To describe
this, several thermodynamic models exist; nevertheless, most expressions
are phenomenological and lead to over-parametrization. They also fail
to describe the influence of sample history and the degree of miscibility
via structure–property relationships. We propose a new model
to deal with semi-compatible the generalized mean model,
which can classify diluent segregation or partitioning. When the constant kGM is below unity, the addition of plasticizers
has hardly any effect, and in some cases, even anti-plasticization
is observed. On the other hand, when the kGM is above unity, the system is highly plasticized even for a small
addition of the plasticizer compound, which indicates that the plasticizer
locally has a higher concentration. To showcase the model, we studied
Na-alginate films with increasing sizes of sugar alcohols. Our kGM analysis showed that blends have properties
that depend on specific polymer interactions and morphological size
effects. Finally, we also modeled other plasticized (bio)polymer systems
from the literature, concluding that they all tend to have a heterogeneous
nature.
Global concerns over climate change, plastic pollution, and scarcity of resources have made several industries actively look for alternative and sustainable material sources. Biopolymers are a great alternative with many applications already developed in food, agriculture, biomedical, and composite fields.^1−3^ However, solid-state materials consisting of polysaccharides and proteins are often too brittle and not workable.^4^ This is a classical materials design dilemma, where films are either (too) stiff and brittle or tough and (too) ductile. A common alternative for toughening polymeric materials is blending them with a diluent.^5−7^ This includes both (co)polymers and small non-volatile molecules, which can be added to decrease the polymer’s glass transition temperature (Tg). Therefore, further exploring our understanding of polymer-polymer and polymer–diluent systems is fundamental for developing improved biodegradable and sustainable biopolymer-based applications.
Biopolymer blends are frequently required because they can combine the specific properties of different materials in one. Often, small molecules are applied to plasticize the biopolymer, which provides better toughness and avoids catastrophic brittle failure. The ideal plasticizer for such biopolymer-based materials must be non-toxic, biodegradable, and preferably derived from natural sources.^4^ For instance, there are many reports of materials composed of polyols, oligosaccharides, citrates, lactates, vegetable oils, and tannins as natural additives.^8−10^ Even though the literature using bio-based materials and plasticizer agents is growing, their application is often investigated by trial and error. Furthermore, very few research studies exist on how to select a plasticizer, with most of them being phenomenological and case-specific. In addition, sample history, miscibility, and the extent of (local) phase separation are ignored. Therefore, how component compatibility affects the barrier, thermal, and mechanical properties of biopolymers is poorly addressed. As a side note, it is probably fair to say that living tissues, materials in nature with structural and mechanical functions, such as teeth, bones, wood, wool, and silk, obtain their sometimes excellent properties by virtue of components that bring about the required amount of mobility.
Polymer blend miscibility is often studied via the determination of Tg, in which a single measured transition temperature identifies compatible systems.^11^ In truth, due to chain connectivity, even in miscible systems, the components will effectively experience distinct levels of mobility or relaxation times associated to a glass transition.^12^ For binary systems, several thermodynamical models for predicting the averaged Tg have been proposed, for instance, using the Gordon–Taylor and Couchman–Karasz expressions.^7,13−15^ In product engineering, the Fox equation^6^ is frequently applied, which also appears as a limiting form of the Couchman–Karasz expression. Nevertheless, it is seldom mentioned that these theories are only intended for the case of full compatibility. This is far from the general case of (bio)polymer mixtures, which may have a complex chemical composition and might show multiple conformations and variable levels of polydispersity. Due to this molecular complexity, the nanostructures that evolve from mixing biomacromolecules and diluents are expected to be locally heterogeneous in composition. On a supramolecular scale, there is local organization of mixed components, i.e., a certain level of segregation or partitioning may be recognized (Chart 1). Experimentally, the Tg of such heterogeneous blends is identified by one broad transition. The prediction of the Tg, even in binary systems, will also be difficult due to possible component interactions.^16^ As a result of concentration fluctuations^17^ and specific interactions, data can show negative or positive deviations from the usual rule of mixing for Tg.
Chart 1 Morphology Classification of Polymer Systems We Propose for Glass Transition (Tg) Modeling Based on the Degree of Miscibilitya^a^ Images inside boxes and circles relate to the microscale and nanoscale, respectively.
Not surprisingly, there have been plenty of reports on how models based on the Couchman–Karasz expression fail to describe systems lacking true miscibility.^15,18,19^ Consequently, data from inhomogeneous mixtures are usually fitted by including additional correction terms to these equations. This leads to phenomenological expressions and over-parameterization. To work with semi-compatible systems, we propose an alternative working model, the generalized mean (linear) or GM(L) model. Within this framework, the conventional Fox equation becomes a particular case of our model, that of a homogeneous miscible system. It is based on the rather obvious idea that Tg is connected to interactions (enthalpy) and degrees of freedom (entropy) using a second-order phase transition-like framework, where the enthalpy and entropy type terms are averaged as a function of composition.
To showcase the use of the GM(L) model, we have performed a systematic study on the general plasticization effects of Na-Alginate with polyols. We have selected sugar alcohols as polyols because they provide a series of increasing H-bonded interactions and sizes. Then, we investigated if a single master curve of plasticization occurs based on a plasticizer’s mass fraction or molar density of the interacting functional group. Additionally, we used this system to investigate the interactions and the degree of miscibility based on our Tg modeling.
Finally, we demonstrate
how the GM(L) model can be applied
to an extensive list of Tg datasets from the literature.
We explore the general understanding of static heterogeneity in (bio)polymer
mixtures by evaluating the model’s constant kGM. Special attention is given to complex, multicomponent
biopolymer systems since we believe the current theoretical background
on Tg for this class of materials has yet to be adequately
addressed.
Sodium alginate (high ratio of guluronic
acid, Mw ≈ 12–40 kDa), ethylene
glycol, glycerol, meso-erythritol, d-(+)-arabitol, d-mannitol, and d-sorbitol were purchased from Sigma–Aldrich.
The alginate-polyol
films were prepared by the solution-casting method. Different sugar
alcohols ((CHOH)n, where n is varying) with increasing chain length were tested to
investigate the plasticizing effect on the developed films. Namely,
ethylene glycol (CH22), glycerol (C3), erythritol
(C4), arabitol (C5), sorbitol (C6), and mannitol (C6) were used as plasticizers. The film
preparation procedure is described as a 5 wt % stock solution
of Na-alginate in demineralized water was prepared. Afterward, an
appropriate amount of dissolved plasticizer (5 wt %, in demineralized
water) was added into separate film-forming solutions at a final dry
mass of 0 to 50 wt % plasticizer (alginate basis, pH 8). The film-forming
solutions with different plasticizer content were carefully homogenized
with a glass rod, avoiding bubble formation until uniformly blended,
and cast into polystyrene Petri dishes. The exact weight was calculated
separately for each plasticizer to result in films with a thickness
of about 0.15 mm. The freshly cast films were placed in ambient conditions
(at 50 RH and RT), and different drying environments were tested.
After around 3 to 5 days of drying, the free-standing films were peeled
from the casting surfaces for analysis. Water is a natural plasticizer
for hygroscopic alginate films, and sorption/desorption phenomena
occur depending on the ambient conditions. Hence, to evaluate only
the effects of polyol addition to the films, the cut film specimens
were vacuum dried for 1 day at 40 °C and kept in a desiccator
containing silica gel until immediately before analysis. For glycerol
and sorbitol, the humid films (ambient, ∼50% RH) were also
analyzed for comparison (Supporting Information, Figure S12 and Table S1).
It was possible to add C2 to alginate and cast thin films. However, vacuum drying also
removed part of this plasticizer from the matrix since it is too volatile.
Hence, to measure the exact C2 content in the dried films,
thermogravimetric analysis (TGA) was carried out on a PerkinElmer
TGA 8000. The measurements were performed on samples of about 5 mg
placed in a corundum crucible from 30–300 °C at a heating
rate of 5 °C min^–1^ under a nitrogen atmosphere
with an isothermal step at 90 °C for 30 min. TGA was also used
for determining the water content in films of C3 and C6 equilibrated to ambient relative humidity using similar scans.
TGA results can be found in the Supporting Information, Figure S5 and Table S1.
Dynamic mechanical thermal analysis (DMTA) was performed on a PerkinElmer DMA-7e. DMTA experiments on the plasticized films were performed in tensile mode at a frequency of 1 Hz, a −100 to 180 °C temperature range, and a heat rate of 5 °C min^–1^ with film dimensions of roughly 20.0 mm × 3.0 mm × 0.1 mm. The thickness of the films was measured with the aid of a digital micrometer. The resulting glass transition was observed by the abrupt change in storage modulus slope and corresponding loss modulus maximum. This event is often called a polymer’s alpha relaxation. When possible, the Tg was estimated from duplicate measurements.
To this experimental data,
models were applied based on a Tg rule of mixing
of polymer and plasticizer contributions. For convention, Tg1 and Tg2 are expressed
as polymer and diluent components, respectively, with high and low Tg values. We chose to fit the often-applied Fox ^6^
where xi and Tgi denote the molar fraction
and glass transition of components 1 and 2, respectively.
Further, we also fitted our model of interest, the generalized mean linear (GM(L)):
where ϕ~i~ and Tgi denote the volume
fraction and glass transition of components 1 and 2, respectively,
and kGM denotes the model constant. A
full description of the Fox model and the GM(L) models we propose here can be found in Appendix A (Supporting Information). Curve fitting using
nonlinear least squares was performed for all the studied plasticizers
using a Python code and the function scipy.optimise.curve_fit, which employs a trust region reflective algorithm.^20^ The Tg values for alginate-polyol were
optimized case by case but allowed to range from −200 to 200
°C. In addition, the Tg of alginate was not
initially constrained to be the same in all systems. No initialization
values were given. The goodness-of-fit of models was evaluated by
the total sum of squares (TSS), p-value, and standard
error of the regression S.
Fox and GM(L) models, eqs 1 and 2, were also tested to an extended dataset of (bio)polymer blends carefully gathered from the literature. For completion, the full GM model was also investigated with alpha and beta values set to be positive (Supporting Information, Figure S15, and Table S3), as this constraint on the exponents is required to ensure convergence.
The glass transition temperature is a dynamic property with great current interest, since it is tied to thermal, mechanical, and vibrational properties. For instance, it is used not only to determine operational and processing temperature ranges but also influences mechanical properties like stiffness, tensile strength, toughness, hardness, and impact resistance.^4,5^ Besides standard thermomechanical factors, it has been related to materials’ adhesive and healing mechanisms.^21−23^ Indirectly, Tg will also affect electrical, optical, diffusion, and barrier properties, physical aging, and environmental stability. The Tg of polymers can conventionally be assessed through thermal analysis, i.e., evaluating the dependence of a specific volume, jump in heat capacity, or change in modulus on temperature.
We chose to study the Tg of alginate-polyols by DMTA due to the high sensitivity of this method to polymer relaxations. The onset of the primary relaxation (alpha) corresponds to the mobility of the main chain, which happens only at Tg. Figure 1 shows examples of alpha relaxation identification from highly plasticized alginate films. In a polymer blend, the presence of one major relaxation is a sign of miscibility. DMTA showed primarily one main relaxation for dried samples, while samples left to ambient relative humidity resulted in the appearance of additional relaxations. This phenomenon is further explained in Supporting Information (Figures S6 to S12). After the Tg event, the magnitude of the rubber plateau in alginate blends varied with the type and size of added sugar alcohol.
Figure 1 DMTA analysis of Na-alginate-(sugar alcohol) films containing 50 wt % glycerol (C
3) or sorbitol (C6). The higher and lower curves respectively show the temperature dependence of the storage (E′) and loss (E″) moduli. The dashed lines demonstrate how to estimate the temperature of a glass transition relaxation on a logarithmic modulus scale.
In Figure 2, the
obtained Tg values of dry blends are plotted against
the diluent’s mass or equivalent molar fractions. Irrespective
of the way the plasticizer content is evaluated, one cannot find a
master curve of Tg versus plasticizer. This is surprising
since sugar alcohols have the same generic chemical (CHOH)n. Even if we reduce all polyol
concentrations to [CHOH] equivalents, as shown in the inset graph
of Figure 2B, there
is no obvious universal Tg pattern. This strong argument
supports that even though they are miscible, the sugar alcohols do
not interact in the same way with the alginate chains. Similar findings
of a plasticizer-dependent interaction and compatibility limit have
previously been reported for the systems of alginate and CH23 and C6 polyols.^24,25^
Figure 2 Glass transition temperature (Tg) of mixtures of Na-alginate and sugar alcohol plasticizers in mass (A) or molar (B) fractions. The sugar alcohols are depicted from C
2to C6, based on the general formula (CHOH)nH2. Inset: Tg over plasticizer fractions translated to CHOH molar equivalents. Error bars indicate standard deviation.
We have performed model curve fitting to evaluate
this Tg data (Figure 3). The widely applied Fox model is a simple harmonic
mean
of Tg contributions. We observe that this model does
not fit the data of most sugar alcohol mixtures well. Even though
the data fit for C3 and C5 are statistically
accurate (p < 0.05, S < 31
°C), the values of Tg are poorly predicted (Table 1). Alternatively,
the linearization of the generalized mean model, GML, shows an excellent prediction of datasets (p <
0.01, S < 15 °C). In addition, the GML goodness-of-fit is equivalent to that obtained via the
analogous Gordon–Taylor equation. However, when possible, the Tg of individual components should also be experimentally
obtained prior to model fitting. Hence, Table 1 values are to be taken as a likelihood of Tg within the mixture. We also note that setting appropriate
boundary conditions for the individual Tg contributions
was necessary for a good-quality GML fit.
Figure 3 Experimental and calculated values of glass transition temperature (Tg) for Na-alginate-(sugar alcohols). (A) Fox model (FOX); (B) generalized mean linear model (GML). Curve-fitting was allowed using appropriate boundary values for the individual Tg parameters.
Another advantage of the Tg models
is that they
can be used to indirectly determine the (virtual) transition of a
glassy polymer by extrapolation to zero diluent concentration. Like
many biopolymers,^26^ the Tg of pristine Na-alginate cannot be determined since thermal decomposition
is observed before the transition. From Figure 3, all alginate-polyol datasets point toward
a virtual Na-alginate Tg or Tg1, between 60 to 180 °C. Russo et al.^27^ have previously reported a Tg of 133 °C
for Na-alginate based on differential scanning calorimetry of relatively
dry specimens. This seems like a reasonable estimate of M-rich alginate
with the remaining tightly bound water. We can use this as a unified
value for the Na-alginate-(sugar alcohol) data and retrofit it to
the GML model (Figure 4). The approximated value of 133 °C does seem
to fit well with most datasets except for C6 (p > 0.05). That can be explained by the fact that the estimated Tg of Na-alginate is not an actual material property but
an apparent one, with a plasticizer changing the internal structure.
For C5 and C6 polyols, both studied models result
in a lower Tg estimated for the neat alginate. It
might be that the addition of a larger H-bonding plasticizer partially
disrupted the semi-crystallinity of this block-copolymer. Evidence
of semi-crystallinity was also found in powder XRD, haziness of alginate-polyol
films, and a high modulus rubber plateau in the DMTA results (Supporting
Information, Figures S1, S4, and S6–S11). Additionally, the plasticizer itself also showed a tendency to
crystallize, as in the case of films with high content of C4 or another C6 compound (mannitol) (Supporting Information, Figures S2–S4).
Figure 4 (A) Experimental and calculated values of glass transition temperature (Tg) for Na-alginate-(sugar alcohols). The generalized mean linear (GML) model was fitted by assuming a fixed glassy polymer Tg (star) and appropriate boundary values for the plasticizer Tg. (B) Illustration showing the difference in steric partitioning of a small or big plasticizer in a semi-crystalline polymer.
Nevertheless, the new GML fits
described all datasets
well as a physical model (S < 25 °C) (Table 2). The fit values
obtained for polyol Tg were in good agreement with
the literature (Supporting Information, Table S2). The retrofit allows us to appropriately compare the alginate Tg over the increasing plasticizer fraction. For small-size
polyols, C2 and C3, the Tg of
the blend decreases rapidly with more polyol until a plateau is reached.
For larger polyols, C5 and C6, we observe a Tg plateau already at a relatively lower polyol fraction.
The GML model introduces a new constant, kGM, which can be interpreted to arise from the
static partitioning of the polymer/plasticizer fractions. From Table 2, the positive kGM values for all Na-alginate-(sugar alcohols)
indicate a substantial deviation from the case of miscibility (kGM = 1, analogous to the Fox model). This kGM value of >1 means that the effective plasticizer
concentration appears to be higher than expected, resulting in a lower Tg at lower plasticizer content due to partitioning. The
most significant deviations were observed for C5 and C6 alcohols, which might be explained by their size, causing
substantial steric interaction-driven partitioning in a semi-crystalline
matrix. We envision that a smaller plasticizer, such as C2 polyol, would better penetrate and fill the free volume of the amorphous
domains in contrast to C5 and C6 (Figure 4B), which would not be able
to penetrate into the amorphous phase adjacent to the crystalline
regions. In fact, it should be noticed that a certain level of semi-crystallinity
will always result in kGM > 1 as the
concentration
of diluent in the amorphous matrix regions will effectively be higher
than expected from the overall composition because the crystalline
regions are not (or much less) available.
The actual extent of semi-crystalline/amorphous fractions and domain sizes is experimentally challenging to be obtained. In theory, it might have been resolved by X-ray scattering and analysis of the crystalline peak width using the Scherrer equation. For the case of alginate semi-crystallinity, the measured crystalline degree would also serve to estimate the amorphous phase that is available for the plasticizer. Thus, this amorphous space would be equivalent to the length of heterogeneity. This rationale obviously assumes the plasticizer to be amorphous in the resulting mixture. Nevertheless, getting good information on this from scattering techniques is very challenging and would constitute an entire additional study. One advantage of the GML model is that the quantification of any crystalline or immobile fraction is not necessary to fit Tg data over composition and identify levels of heterogeneity, therefore, it might serve to better determine heterogeneity from structural analysis as it provides an expectation value.
Indeed, only the GML model resulted in good descriptive
curves for the Tg of alginate-(sugar alcohols). We
believe that this can only be due to partial miscibility or, to put
it in another way, local heterogeneity of polymer and plasticizer
distribution in such blends. In some cases, the components’
specific interactions might cause this phenomenon, i.e., semi-crystallinity,
H-bonding, and chirality. In fact, H-bonds are well known to affect
the final semi-crystallinity of polymers.^28−30^ Another influence
might be the chirality of C4 to C6 sugar alcohols,
causing preferential sites in the plasticizer distribution. In general,
the case of alginate blends is a good example that specific interaction
contributions and partitioning need to be considered. The Fox model
neglects such interactions as it is based solely on the entropic contributions
of components in a fully miscible blend. However, fully and partially
miscible blends can be described with GML, where
the constant kGM acts as a factor representing
the heterogeneity. Regarding thermodynamics, kGM can also be interpreted as a convoluted factor of both (second
order) enthalpic and entropic contributions.
Other situations can cause static
heterogeneity (kGM ≠ 1) of a diluent
distribution within a glassy polymer matrix. A link to the Tg property can easily be interpreted if coupled with the
free volume theory. For comparison purposes, one could classify heterogeneous
blends resulting in kGM below or above
unity, as illustrated in Chart 2. Both semi-crystallinity and crosslinking density variations
can result in Tg values lower than predicted by the
Fox model (kGM > 1). In the first case,
as shown here with alginate-(polyols), steric partitioning effects
can happen if the glassy matrix forms some crystalline or densely
packed domains. With regards to cross-linking, a densely packed polymer–polymer
network can also effectively create irregular boundaries to plasticizer
clusters,^7^ even though cross-linking generically
increases Tg, the plasticizer would be at a higher
concentration in the available regions (Chart 2).
Chart 2 Illustrations of a Homogeneously Distributed (k
GM= 1) or Partitioned Diluent (kGM≠ 1) in a Glassy Polymer Hosta^a^ Boxes: microscale; circles: nanoscale.
A few examples, usually in a low
diluent content regime, can lead
to Tg values higher than predicted by the Fox model
(0 < kGM < 1). For instance, often
at lower volume fractions, a plasticizer with a tendency for segregation
can result in the free volume cavities of the polymer being filled
with plasticizer, e.g., the anti-plasticization effect. It can also
happen that interactions between the diluent/plasticizer and stiff
polymer chains will enhance the level of polymer packing.^31^ This is analogous to the anti-solvent polymer
packing effect.^32^
In both cases,
further diluent clustering will frequently lead
to microscopic phase separation of a blend, which is often observed
in the form of opacity and coarsening of the phase-separated structure.
Further, the diluent phase will either exudate out of the solid matrix,
forming a binary or ternary-phased system, or even locally crystallize,
thereby removing the plasticizer from the polymer matrix entirely.
These two events are macroscopic. From a thermodynamic perspective,
the kGM factor can also characterize blends
from miscible to immiscible states as it deviates away from unity.
It is interesting to note that the proposed local heterogeneity is not necessarily an undesirable phenomenon on a micro- or nanoscopic level. Heterogeneous plasticization will create zones of local plasticization and lubrication of amorphous polymer chains, resulting in mobility, pliability, and increased toughness. Simultaneously, the material’s structural integrity or tenacity is still provided by the regions of low plasticizer content, preventing creep and flow. In other words, good plasticizers should not be too compatible with the polymer. It should be enough to mobilize without solubilizing the whole system.
Within the context of binary polymer blends, it might be helpful
to consider the self-concentration approach proposed by Lodge and
McLeish (2000) for blends with large Tgi difference.^12^ The theory states that
the average composition of the local environment around a certain
component must be enriched by itself because of chain connectivity.
Therefore, even for homogeneous blends, each polymer will effectively
experience its own composition dependent dynamics and effective Tg. This unavoidable segregation happens at the level of
the chain Kuhn length and can get further exacerbated by the abovementioned
specific interactions and clustering/segregation phenomena. The kGM constant is obtained assuming a mixture’s
single or averaged Tg, where the product kGMϕ2 is an estimation of the
(anti)plasticizer phase. Therefore, kGM is also a convoluted expression of local heterogeneity from multiple
length at chain segment and cluster levels. A theoretical
relationship between the effective self-concentrations of a polymer/diluent
in a blend and the GM(L) model constant
is still lacking, which shall be considered in future work.
In this
section, we demonstrate the versatility of the GM(L) model for polymer blends of synthetic and biological
origin. The goal is to show via partitioning factor kGM how easily systems fall outside true miscibility and
simple rule-of-mixing theory, especially when biopolymers are used.
These peculiar states of miscibility can arise from strong specific
molecular interactions, steric effects, and conformational changes
(morphology), depending strongly on sample history. It also makes
sense to present this data compilation to connect our current work
to general plasticization and anti-plasticization phenomena.
Figure 5 displays
datasets with a greater decrease of Tg with diluent
content (kGM > 1) in contrast to what
was predicted by Fox’s theory. We can interpret those results
with the main rationale that the effective diluent volumetric fraction
in a polymer matrix is higher than initially expected. In Figure 5A, the synthetic
polymer blend of Phenoxy resin or poly(hydroxy ether of bisphenol-A),
with an aliphatic polyester of succinate (PDPS), shows decreased Tg values in comparison with those predicted by entropic
contributions (Fox theory).^31^ It is common
knowledge in polymer processing that a physical blending of polymers
needs strong specific interactions to result in miscibility. In this
case, H-bonding between carbonyl groups of succinate ester and hydroxyl
of Phenoxy should overcome intramolecular cohesion and favor miscibility.
However, the Tg curve gives us additional information
that there must be competing energetic interactions since kGM > 1. We speculate that this makes sense,
since while Phenoxy is a blocky and amphiphilic polymer, the succinate
polyester is polar, which might cause a more loosely packed structure,
thus affecting the free volume of the blend.
Figure 5 Experimental and calculated values of glass transition temperature (Tg) for several datasets displaying a greater-than-expected decrease with a plasticizer (or k
GM> 1). (A) Synthetic polymer blend of the polyhydroxyether of bisphenol A (PHENOXY) and poly(2,2-dimethyl-1,3-propylene succinate) (PDPS). (B) Biopolymer-(plasticizer) mixtures. FOX: Fox model (dotted lines); GM Linear: generalized mean linear model (solid lines). Curve-fitting was performed using fixed values for the individual Tg parameters for demonstrative purposes. Data from Schneider, 1997;^31^ Chang, 2006;^33^ Linnenkugel et al., 2021;^15^ and Tabary et al., 2016.^37^
The plasticized mixture of tapioca starch-(glycerol/water)
also
follows a kGM > 1 trend (Figure 5). The difference between Fox
and GML curves is subtle, as seen in Table 3. However, this becomes relevant
if we know that the films formed a semi-crystalline matrix upon drying,^33^ possibly resulting in plasticizer partitioning.
In starches, the recrystallization of amylose and sometimes amylopectin
can fundamentally influence properties, e.g., water vapor permeability
and toughness. Water from moisture can further change Tg considerably.^34,35^ Consequently, the effect of water
in crystalline biopolymer blends should always be evaluated or excluded.
Continuing on Figure 5B, the system of maltodextrin-glucose^15^ is interesting because the polymer is a polydisperse derivative
of starch. The maltodextrin analyzed did not show crystallite sites;
nevertheless, again, we find that kGM >
Complexes of guest–host chemistry and cross-linking will also impact Tg values and trends. In Figure 5B, a blend between a methylated polymer of β-cyclodextrin (polyβ-cyclodextrin) and mannitol^37^ shows a significant divergence from Fox’s prediction. The polymer cyclodextrin can form hydrophobic-core inclusion complexes for drug delivery. The degree of di-ester cross-linking of the polymer with citrate is also essential to this application and Tg determination. The 36 wt % cross-linked and plasticized material was produced via a melting process. We could relate the Tg divergence from the ideal rule of mixing theory to the increased free volume of heterogeneous cross-linking of the sample, influencing molecular packing, along with mannitol’s resistance to filling in the hydrophilic core of cyclodextrin inclusions.
A good plasticizer will result in pliable and durable materials
that are easy to process by increasing the mixture’s free volume
or lowering the Tg. In turn, the mixed material should
be tougher than the initial glassy polymer. In Figure 6, datasets show an increase of Tg with polymer or plasticizer content. This increase deviates completely
from the Fox theory; for GM(L),
it represents the case of 0 < kGM <
1 (Table 3). In fact,
the synthetic blend of polybenzimidazole with commercial polyetherimide
(Ultem)^31^ resulted in anti-plasticization.
This phenomenon happens when we observe an increase in overall specific
density with diluent addition.^5^ In extreme
cases, even phase separation can occur. Within the partial miscibility
region, anti-plasticization can be desired if a material’s
performance needs to be improved. However, a slowly decreasing Tg or even a plateau with increasing diluent content often
seems counterintuitive. Polybenzimidazoles (PBIAz) are high-performance
engineering thermoplastics with very stiff aromatic polymer cores
and high Tg values (> 400 °C). In Figure 6A, we propose that
the strong
H-bonding interaction of PBIAz with Ultem via amine groups may cause
additional stiffness via chain confinement. Hence, in this case, the
favorable interactions between the chains cause the Tg to hardly decrease, giving rise to anti-plasticization.
Figure 6 Experimental and calculated values of glass transition temperature (Tg) for several datasets displaying lower than expected decrease with a plasticizer (or 0 < k
GM< 1). (A) Synthetic polymer blend of polybenzimidazole (PBIAz) and Ultem polyetherimide (Ultem). (B) Biopolymer–(plasticizer) mixtures. FOX: Fox model (dotted lines); GM Linear: generalized mean linear model (solid lines). Curve-fitting was performed using fixed values for the individual Tg parameters for demonstration purposes. Data from Schneider 1997;^31^ Sahari et al., 2013;^38^ Ma et al., 2019;^40^ and Liu et al., 2013.^45^
For sugar palm starch-(glycerol) plasticized films
(data in Figure 6B),
strong H-bonding
interactions between glycerol and amylose/amylopectin resulted in
high Tg values.^38,39^ In particular,
for starches, processing can be crucial. Starch samples often must
be gelatinized at high temperatures (>130 °C) to obtain thermoplastic
behavior. This could result in the plasticizer affecting the formation
of crystalline domains from starch moieties. Similarly, systems of
chitosan-polyols can also show significantly different properties
depending on the strength of H-bonding interaction with the polymer
backbone and overall moisture content (Figure 6). The chitosan data is shown with respect
to the hydroxyl groups of sugar alcohols.^40^ It is important to note that with further diluent addition, aging,
or the increment of water from moisture, systems can dramatically
move from the anti-plasticized to the plasticized regime.^41−43^ This can be observed both in Tg and in mechanical
performance. The plasticization shift will depend on how strong the
energetic interactions (enthalpy-driven) are and how favorable the
increase of free volume (entropy-driven) is. In polymer blends and
plasticized systems with large ΔTgi, this has been early on reported as a break (or cusp) in Tg-composition curves.^11,44^ The phenomena
have mostly been attributed to a critical temperature, where a change
in (strong) specific interactions with diluent fraction is observed.
Trends in multicomponent systems can also be interpreted similarly
via kGM. A 1 starch/chitosan blend was
produced by microfluidization.^45^ This blend
was plasticized by glycerol and water, showing high anti-plasticization
(0 < kGM < 1) through strong H-bonding
between the plasticizer and macromolecules. Previous works have only
presented explicit thermodynamic solutions for multicomponent systems
of polysaccharides, polyols, and water^8,15^ by working
with Flory Huggins’s free volume theory and extending the Couchman–Karasz
expression for Tg.
Locally heterogeneous mixtures
are ubiquitous in materials based
on (bio)polymers, showing complex thermodynamic behavior. We have
observed that kGM can be a helpful tool
to investigate (bio)polymer-diluent miscibility and possibly derive
insights into structure–property relationships. We note that
the linearized GML model is intended only for systems
in a continuum, i.e., with no phase separation, crystallization, or
phase inversion. Alternatively, the original GM model
can adopt complex shapes (Supporting Information, Figure S15). Yet, we do not recommend modeling immiscible
systems instead of splitting the developed phases. Overall, this study
is another example that the topic of glass transition is a complicated
part of polymer science.^46^ For example,
it is often very challenging to determine the Tg of
neat and biopolymer mixtures because the thermal transitions are found
above degradation, increasing with the strength of electrostatic interactions,
cross-links, and branching. Nowadays, this topic has become even more
relevant with the rapid pursuit of tailored biodegradable and sustainable
materials.
The generalized mean linear
model, GML, works
as a versatile model for studying the glass transition of polymer
blends and plasticized systems. The model can be seen as a natural
extension of the widely used Fox model (1956). In GML, if the constant kGM is not 1, the system
is not fully homogeneous—or Fox-like—and there is obvious
evidence of heterogeneity or local demixing on a nanoscale. This can
be explored via systematic studies to reveal the structure–property
relationships of blends and elect a suitable and stable plasticizer
for a specific application. To deal with strong interactions and heterogeneity,
previous models have been proposed and modified, like Couchman–Karasz
equations. However, the adopted solutions are often case-specific,
phenomenological, and lead to over-parametrization, thus failing to
describe the overall picture of (partial) miscibility.
This study showcases our GML model applied to predict the Tg of Na-alginate and polyols as plasticizing molecules. The experimental data on Tg clearly does not follow the Fox equation, while only the GML model can fit the results. This indicates that heterogeneity is important in alginate-polyol, as is also substantiated by the observed size effect of the type of polyol on Tg curves. This proposed heterogeneity indeed becomes apparent at higher plasticizer content from the overall sample appearance and via microscopy. Hence, sample processing history also becomes important. This heterogeneous plasticizer distribution is presumably caused by regio-specific interactions in the alginate-polyol system, such as the semi-crystallinity of the polymer matrix and steric effects in amorphous domains, as is apparent from our results. In addition, the GML model can easily describe the heterogeneity present in a wide range of diverse (bio)polymer blends, demonstrating its utility in analyzing complex polymer materials and even anti-plasticization phenomena.
Based on the above and considering the heterogeneous nature of biopolymers, research on bio-based systems can benefit from the GML approach. Living organisms produce biopolymers that are designed to be complex in structure and interactions, containing chiral macromolecular arrangements taking the form of helices and sheets or even showing semi-crystallinity. The already-present structural heterogeneity is often amplified by extraction and (re)processing conditions. In the case of solvent-based processes, the scale of heterogeneity can be large, especially if elevated temperatures are used. The chemical structure, therefore, is not so well-controlled. In addition, electrostatic interactions are nearly always present, which adds additional specific interactions not customarily found in fossil-based polymers. In summary, one could say that the molecular morphology of materials based on biopolymers and natural plasticizers is intrinsically heterogeneous. Hence, such systems should nearly always fall outside the commonly used rules of mixing for the thermal properties of polymer blends.
We thank the Netherlands Organization for Scientific Research (NWO) for financing this study. We are also thankful to Dr. Jure Zlopaša for data curation and meaningful discussions on plasticization.
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.biomac.2c01356.
The manuscript was written with the contributions of all authors. All authors have approved the final version of the manuscript.
This work was financed by the Netherlands Organization for Scientific Research (NWO), Earth and Life Sciences Division (grant number ALWGK.2016.025).
The authors declare no competing financial interest.