Properties of one and the same polymer can vary greatly with the history of a sample, reflecting its memory of past events. I propose that this remarkable changeability of polymer properties can be related to the immense variability of non-equilibrium conformational states, providing polymers with capacities for responding and adapting to changes in environmental conditions and to external stimuli. By decoding the relations between properties and meta-stable conformational states, we may be able to accomplish polymer products with selectable unique properties. In support of this claim, I first present a few typical examples focusing on changes induced by varying drying, freezing, or crystallization procedures, relevant in many industrial processing strategies for polymeric systems. In these examples, deviations from equilibrium conformations are controlled by a preparation parameter and the annealing/aging time and temperature. Subsequently, I briefly discuss the possibilities for a quantitative description of chain conformations deviating from equilibrium, which allow establishing a link between changes on a molecular level and their macroscopic behavior. A comprehensive and systematic investigation of out-of-equilibrium polymer properties will widen the scope of polymer science and enlarge the range of applications of polymers based on their responsiveness and adaptability derived from their memorizing capacities.
I. WHAT CHARACTERIZES MEMORY?
Properties of polymeric materials may depend strongly on sample history. Thus, appropriate experimental protocols may decide the behavior of a polymer.1 For example, quickly cooled and slowly cooled polymer samples may (and often do) exhibit different properties and relaxation behaviors.2–7 This dependence on sample history results from the fact that the polymers could not (fully) equilibrate and thus did not “forget” their history. Reflecting experiences of the past, the properties of such non-equilibrated polymers often differ significantly from the properties they possess in their equilibrated state, and thus, these deviations may be considered as their “memory” (Fig. 1).
Here, the term “memory” signifies the ability to establish a link between past and future in terms of material properties. Such memorizing capacity of polymers implies the potential to respond in different ways to external stimuli according to experience gained in the past. Thus, such memory can be considered as information, which was encoded by processes in the past (shear, temperature variations, and exposure to light), stored via changes in conditions (rapid change in temperature or concentration), and can be retrieved through appropriate stimuli applied to these materials. Borrowing from Shannon’s relation between information and entropy (entropy is missing information),8–10 we may relate the memorizing capacity of polymers to their conformations, i.e., the arrangement of their sub-units (monomers) in space. We may define information “memorized” in a polymer as the knowledge about which conformations are not possible (realizable), taking as a reference the set of all possible conformations of the polymer corresponding to the concept of a random walk.11,12
Memories are often non-permanent. The generated and stored information may change in the course of time, i.e., memories may fade away. In addition, encoded, stored, and retrieved information can be corrupted in a number of ways. Employing appropriate annealing and relaxation steps may also cause erasure of information (“forgetting”). However, at the application temperature, the time required for erasing preparation-induced meta-stable states and reaching thermally equilibrated states may be exceedingly long. Consequently, many polymer samples are never fully equilibrated and thus “remember,” at least to some extent, their (thermal and mechanical) history, including the ways in which they were prepared.
The process of equilibration is to some extent related to ways of “forgetting,” i.e., re-establishing all the missing conformational states. A fully equilibrated polymer does not contain any information and has no memory of past events. We may call it a “dead” or “passive” polymer. Upon equilibration, the material becomes homogeneous and the parameter measuring homogeneity, the entropy, will be maximized.13 According to Shannon, the lower the entropy, the higher the content of information. Translated to polymers, when the conformational entropy is lower, with less “free” choices of conformations and the more defined (oriented and correlated) chain conformations, we possess more information about the polymers. A fully stretched chain represents the highest content of information. All bond angles are well defined, and no choice between different conformations remains. Here, we suggest classifying the information content of polymers by how strongly their conformations deviate from their equilibrium ones. Thus, a suitable parameter for quantifying such deviations on a molecular scale may be related to the corresponding amount of decrease in conformational entropy. Accordingly, the random coil of an ideal chain does not possess any memory because in such a chain no monomer has any information on the orientation of any other monomer.
The capacity to remember past events provides possibilities of learning and allows for adapting and evolving material properties. Thus, materials with memorizing capacities can be understood as information processing systems through the short- and/or long-term impact of their changeable properties.
Having related polymeric memories to conformational states with different degrees of deviation from equilibrium, I now discuss how such deviations affect (averaged) physical properties such as elastic modulus, transition temperatures, optical appearance, or shape, which are observable through measurements on macroscopic scales. The goal is to establish a link between molecular features representing the encoded information and macroscopic signatures (stiffness, optical anisotropy, and melting or nucleation behavior) of this stored information. As polymers allow changes in chain conformations over a wide range of length- and timescales,14 we can expect that macroscopic properties change over a similarly wide range.
II. HOW CAN WE GENERATE MEMORY?
Based on the central assumption that memory of a polymer is related to chain conformations deviating from equilibrium, various physical processes exist, all involving some investment of energy, which can generate such memory. For example, polymer chains can be deformed through the application of external forces (applying a load, shearing, drawing, extrusion, and gel-spinning). Furthermore, conformations can be altered by annealing or aging, or by changes of conditions in the course of sample preparation. If, when processing polymer samples, we do not provide the time required for complete equilibration, deviations from equilibrium remain. Either during sample preparation or during attempting equilibration via a post-preparation treatment, conformations can be (temporarily) trapped in meta-stable states that can store (some) information for a finite, but possibly very long time. We may distinguish between imprinted information already present right after generation of the non-equilibrium state and learned information (grown knowledge) established through attempts to get to the equilibrated state like in the course of appropriate annealing or aging steps. Thus, when measuring polymer properties, the results, i.e., the stored information, may depend not only on how the sample was prepared but also, and sometimes even most importantly, on its previous thermal or mechanical treatment. In short, the ways we produce, store, or exploit polymers have a strong influence on their properties. For example, during industrial processing or when probed under non-linear experimental conditions, polymers may experience strong flow fields. Picking out one test chain in a sea of other chains, all exposed to the same shear field, we may observe chain deformations that deviate strongly from the path of a random walk (Fig. 2).
In contrast to materials made of small molecules, polymeric materials possess a tremendous advantage. Polymers can change their “size and shape” by adopting their conformations across many length-scales without losing their identity, i.e., without “breaking apart.” Such changes in conformation and the possibly resulting meta-stable states are associated with a plethora of relaxation times.15 Highly non-equilibrated chain conformations established in rapidly processed polymeric systems often involve enormously long equilibration times.16,17 Furthermore, the lifetime of meta-stable states may reach values that are so large that some (or all) properties of the sample do not change on the timescale of the experiment and sometimes can be even longer than the service life of the material.18
If we possess ways to control changes in polymer conformation, both in space and in time, we can reach the target of establishing meta-stable conformational states with a tunable degree of deviation from equilibrium. To this end, we can rely on processing steps occurring on timescales that are (significantly) shorter than intrinsic relaxation routes. In the course of sample preparation, characteristic relaxation times may vary, often by orders of magnitude, through changes in temperature (cooling) or polymer concentration (solvent evaporation), making equilibration eventually impossible. In addition, we may cause deformations of polymer chains through (shear) forces acting on the chains in the course of processing. The resulting non-equilibrium conformations can be related to the invested energy. If we would allow for equilibration, all the energy invested will be dissipated either through an increase in conformational entropy or via transformation into heat. Consequently, given that relaxation processes were too slow to re-equilibrate the chains, variable meta-stable states differing in conformational entropy may be realized.
Once the appropriate and desired conformational states are achieved, we need to conserve these states by suitable changes in processing parameters.19 Here, I would like to focus on three possibilities, drying–freezing–crystallizing, being aware that many more exist. I have chosen these three examples because the underlying basic physical phenomena are highly relevant in many industrial processing strategies for polymeric systems. Polymeric materials containing stored non-equilibrium chain conformations should possess the capacity to respond to changes in environmental conditions in a predictable way, opening up new possibilities in employing polymeric systems as smart and programmable materials.
A. Rapid solvent evaporation (preparation parameter)
Many polymeric products are prepared from (dilute) solutions. In comparison to polymer melts, starting from solutions enables fast processing because of the significantly lower viscosity. However, as the final product should not contain any solvent, solution processing necessarily involves a stage of solvent removal. There, fast evaporation of the solvent often provides a possibility for generating and storing “polymeric memory states.”20,21 In the course of solvent evaporation, polymer chains undergo a transition from swollen coils of randomly oriented monomers to a glassy state of incompletely interpenetrating and often partly collapsed coils.22 As the polymer concentration increases in the course of solvent evaporation, the equilibration process slows down and eventually becomes impossible when the drying polymer solution passes a glass transition.23 Accordingly, the precise conformational states depend crucially on how much equilibration of chain conformations was possible during the drying process. It has been demonstrated that various properties of polymer films can be tuned by orders of magnitude when preparing them along appropriate pathways characterized by a dimensionless preparation parameter, which, in essence, is a measure of the time provided over the time required for relaxing chain conformations [see Fig. 3(a)].22 Due to the reduction of relaxation possibilities at increasing polymer concentration, the resulting non-equilibrated chain conformations may become oriented, aligned, and coupled. Particularly for crystallizable polymers, this may introduce transient correlations between polymers, reflected in lifetimes orders of magnitude longer than the longest relaxation time of the same polymer in equilibrium [see Fig. 3(b)].16
B. Quenching below the glass transition or melting temperature
Even if a polymer melt was initially well equilibrated, it may be driven into an out-of-equilibrium situation by a rapid change in temperature, accompanied by a rapid decrease in mobility. Cooling below the glass transition temperature also allows freezing-in chain conformations that have not yet been equilibrated. Depending on the rate of cooling, polymer chains are not capable to perform the required conformational changes on all relevant length-scales (segments, entanglement strands, and whole chain) in order to adapt to the associated thermal contraction and the changes in density, effectively generating non-equilibrated chain conformations.24,25 Thus, we may anticipate that in addition to heterogeneities in both static and dynamic properties, which are characteristic for glasses of small molecules,26–29 non-equilibrated chain conformations induce forces acting upon chemically connected chain segments and between entangled or otherwise correlated neighboring polymer chains but also on a longer length-scale between heterogeneous domains. Such deviations from a homogenous state were demonstrated indirectly by crystallizing a non-equilibrated polymer melt, which was annealed for various times above the equilibrium melting temperature. There, the number of nucleation sites, possibly related to some of the heterogeneous domains, decayed exponentially with annealing time [see Fig. 3(c)].30 Furthermore, if interactions with slippery substrates16 and/or (local) variations in shear forces come into play,31 not all chains will experience the same forces, often generating strong gradients in forces acting on chains. A typical example in this context is melt-extrusion. There, parameters such as flow-rate, temperature gradients, or wall-slip may affect polymer properties significantly.32
C. Meta-stable crystalline states
Probably, the most noticeable cause for metastability of polymeric systems is related to the kinetics of crystallization. The rate of crystallization controls how perfectly chain segments are arranged in crystalline domains. Most importantly, mechanical properties such as the elastic modulus depend strongly on the size and arrangement of crystalline domains and their interconnections.1 Typically, polymer crystallization proceeds at rates too fast for achieving equilibrated conformational states. As the consequence of fast crystallization kinetics and the connectivity of segments, lamellar crystalline structures are generated, exhibiting often quite complex morphologies. These structures are prone to changes during crystallization but also at later stages. The transition from randomly coiled chains in the equilibrated melt to aligned and highly ordered chains in crystalline domains proceeds so rapidly that polymers are not able to adopt the energetically most favorable state.33 Besides ordering of crystalline sequences (stems), processes such as chain folding or the formation of chain loops may lead to inhomogeneities, for example, with respect to the entanglement density.34 Tie chains may connect crystalline domains. Thus, as a function of crystallization conditions, various meta-stable states are obtained, which consist of polymer chains with different degrees of order, all deviating from a random coil conformation.35
Polymer crystals are formed in a sequence of steps, which control morphologies and thermodynamic parameters such as the melting temperature.36 Typically, under conditions of strong undercooling or high super-saturation, even single crystals are expected to possess a branched or dendritic morphology.37 Nonetheless, many polymer crystals grown under such conditions of undercooling/super-saturation exhibit a faceted morphology. Even if the final crystal may appear as a “perfectly faceted single crystal,” it may remember its formation in steps and consequently may melt in steps. As verified through persevering annealing experiments38 and systematic growth studies,39 thin lamellar polymer crystals of a simple faceted geometry may result from a branched morphology, where the gaps between the branches are filled up at later stages by polymers diffusing on the amorphous (non-crystalline) fold surface. Thus, faceted crystals remember their formation stages as can be confirmed by prudently annealing these crystals in steps. The first formed branched (and probably better-ordered) crystalline structure melts at a higher temperature than the polymers integrated later into the crystal. Therefore, this branched morphology “survives” annealing at temperatures below its melting temperature, representing the memory of sequential crystal formation.38
Even single crystals derived from a thin molten polymer film do not melt at a single temperature but rather exhibit differences in melting temperature with a clear gradient from the boundary (growth front) toward the nucleation center. However, although the melting temperatures may be different, all remaining crystalline fragments “remember” that they belonged to the same initial single crystal, as expressed by their unique orientation. The corresponding “cloning procedure”40 (one initial single crystal can be transformed in a multitude of smaller but uniquely oriented crystals) is a remarkable and characteristic feature of polymers.
Another unique feature of crystallizable polymers is the possibility to form so-called “shish-kebab crystals” from sheared melts or solutions.41,42 There, some polymer chains are stretched in the shear-flow direction, which then serve as nucleating agents (shish) for a multitude of lamellar crystals (kebabs), all growing perpendicular to the orientation of the shish. Aligning the “shish-polymers” and increasing their number density finally lead to materials with fully aligned and highly stretched polymers only, yielding impressive mechanical properties with an elastic modulus close to the limiting value resulting from breaking carbon–carbon bonds.43,44
Semi-crystalline rubbers are highly fascinating materials with respect to their high capacity of memorizing experiences made in the past. Deformed meta-stable chain conformations with long relaxation times under ambient conditions can be achieved in a controlled way by first stretching the rubber at elevated temperatures and subsequent appropriate cooling step(s). There, some segments can crystallize, allowing to preserve the deformation, and thus, the energy invested in deforming the chains for long times. Finally, a large amount of this energy can be regained upon melting the crystalline domains. The degree and the rate of re-contraction as well as the temperature at which the rubber will contract can be programmed.45–47 If deformations are applied at different temperatures and in a sequence in different directions, the resulting contraction of the sample will follow the reverse path of the deformation as typically observed in so-called shape memory polymers.46–50 During the induced shape changes, some memory may remain and some deviations from equilibrium may be preserved, which introduce a (partial) reversibility of the contraction, i.e., re-elongation upon cooling. It is quite intriguing that even after having molten crystalline structures, the resulting melt can preserve a memory of the crystalline state. Due to the broad range of melting temperatures of polymer crystals, some (small) crystalline structures may resist the melting process at temperatures below the equilibrium melting temperature. These crystalline remnants can act as seeds for re-growing crystals with the same orientation as the molten original crystals [see Figs. 3(c) and 3(d)].40 However, the most surprising observations are made when all crystals are molten above the equilibrium melting temperature. There, (some of the) molten chains may preserve their orientations and correlations established in the crystals over times much longer than the longest equilibrium relaxation time. This so-called melt memory of crystallizable polymers is a striking example showing that non-equilibrated chains remember their past. All memory is lost when polymer crystals are molten and kept above the equilibrium melting temperature for sufficiently long times.40,51–55
III. HOW CAN WE QUANTIFY MEMORY?
Experiments make it obvious. Sample history, i.e., processes that have been experienced in the past, can influence many polymer properties. However, it is far less clear which parameters allow a quantitative description of what happened in the past and how polymer properties depend on these parameters. Here, as a promising approach to gain insight and to describe the corresponding modifications on a molecular level, I suggest that changes in chain conformations are responsible for the memorizing capacities of polymer systems. Unfortunately, we are not yet able to predict satisfactorily how and to what extent polymer conformations can and will be modified during processing, how conformations change during storage, or how conformations evolve during the use of a polymer. To this end, we need to explore how polymer chains change under the action of various forces, hoping that eventually we will be able to understand the various molecular relaxation processes on all relevant length- and timescales, which determine the observed variations in properties. Results from systematic experimental studies may provide the basis for the development of theoretical descriptions of the corresponding conformational states, which will allow the prediction and quantification of the meta-stable memory states generated by the various processes.
Here, metastability refers to transient states of a certain lifetime related to an activation barrier that must be overcome in order to change to another state. An under-cooled liquid phase may be meta-stable with respect to nucleation and growth of a solid phase (first-order phase transition of crystallization). After equilibration, the solid phase coexisting with a liquid environment represents the minimum in free energy. We anticipate that the metastability of homogeneously deformed chains, achieved, for example, by shearing or extruding a melt, may imply a transformation of these chains into two coexisting sections differing markedly in conformations. The occurrence of “stems” and “flowers,” i.e., the coexistence of a strongly elongated part (stem) separated by a rather sharp boundary from a coiled part (flower),56 may be taken as a characteristic signature of such coexistence. Regions of distinctly different conformations within a single polymer are predicted for the coil–stretch transition occurring under appropriate flow conditions.57,58 Experimentally, Wirtz59 and also Perkins et al.60 observed such a coexistence of two types of conformations within a single polymer chain (Fig. 4).
A similar transition has been predicted for a collapsed polymer chain in a bad solvent subjected to a stretching force, yielding a weakly deformed globular part coexisting with a stretched string of small blobs.61 Related predictions were made for polymers pulled by one end through a melt, a network, or a gel.62 In general, coexisting conformational states may be expected when the total force acting on a chain depends on its conformation. For example, in a sheared polymer solution, the total frictional drag force acting on a chain moving in a solvent may be lowered when stretching the chain.57,58 However, there is a prize to pay. The stretched chain possesses a lower number of possible conformations, i.e., a reduced conformational entropy. Therefore, without changing the total free energy, the system can choose between reducing viscous drag and reducing conformational entropy by partially stretching the chain in the flow direction. Above a certain critical applied force, a multitude of states of differently stretched and coiled chain segments will coexist, all having the same free energy but distinguishable in conformational entropy. One does not have to increase the force any further to change conformations from a mostly coiled to a highly stretched state, i.e., there is no unique correlation between the force acting on a chain and the resulting conformation. However, as monomers belong either to the stretched or to the coiled domain, monomers become distinguishable. Thus, the applicability of the central limit theorem63 for determining the most likely chain conformations becomes questionable.
In order to appreciate the significance and relevance of distorted chain conformations, it is useful to compare them to conformations of polymer chains in equilibrium. In an equilibrated melt, a flexible chain changes its shape constantly due to the Brownian motions of the monomers, agitated by the random impact of neighboring monomers. Thus, averaged over time and applying the central limit theorem, conformations of a single polymer chain follow the statistics of a random walk, yielding a Gaussian distribution of the end-to-end vector of the chains. In the course of time, conformations of polymers fluctuate around a mean value. However, in most cases, the knowledge of the average coil shape is sufficient for the description of equilibrium properties. Like in an ideal gas, where we do not require the knowledge of the velocity of the individual molecules, we do not require any knowledge on particular conformations or fluctuations of chain conformations nor do particular conformations dominate the overall behavior.
Polymer chains in an equilibrated melt behave as if no other chains were present in the surrounding, a behavior represented by the concept of an ideal chain (“chains do not see each other”). The validity of the concept of “freedom of choice” of conformations (each monomer can—like each step in a random walk—choose its orientation in space independently) is based on the central assumption, like in an ideal gas, that monomers do not interact and thus do not affect each other. Accordingly, there is no correlation in the orientation of monomers along a chain and no “communication” with monomers from neighboring chains. All forces acting on any monomer, averaged over time, are balanced, i.e., there is no “pulling” or “pushing” on the chain and between chains.
However, in a non-equilibrated polymer melt containing a significant number of stretched or compressed chains and possibly the coexistence of coiled and stretched parts along individual chains, polymers may and probably do not behave like ideal chains. Due to distortions, net forces are acting on the chains that try to bring them back to equilibrium and, on that way, may deform the chains even further. Thus, in samples with processing-induced non-equilibrated chain conformations, some or all monomers will experience unbalanced forces. These forces may either act “directly” along the backbone of a polymer chain through the connections (chemical bonds) between monomers or act “indirectly” between neighboring polymers through interactions across topological constraints (“entanglements” and “knots”). The strength of these forces may vary in space and fluctuate in time. Summing up all such unbalanced forces resulting from non-equilibrated chain conformation across the whole size of a macroscopic sample, we have to expect that we can observe “net” forces on a macroscopic level. Often, these forces are summarized with the term “residual stresses.”
If the independence of all monomers is not given, the central limit theorem cannot be applied. Thus, a key assumption of the concept of an ideal chain is not fulfilled. Non-equilibrated meta-stable polymer chains most likely cannot be described as a sequence of uncorrelated monomers, neither when they belong to the same chain nor when they belong to neighboring chains. If conformations are not obeying the concept of a random walk with each step being independent of the previous ones,63 the arrangement of sequences of monomers may be correlated in space and their motion can only occur in a concerted, cooperative fashion (correlations in time). For polymer chains having out-of-equilibrium conformations, we cannot exclude that neighboring chains are (partially) aligned with respect to each other. Alignment possibly leads to an effective coupling of chains by the sum of (weak) interactions between the monomers in the aligned sequences, resulting in a cooperative behavior of this ensemble (cluster) of linked chain segments. For example, alignment of chain segments may be introduced via a directional force like in shearing or through gradients of various kinds.
For spatially correlated chains, the degree of coupling of polymer segments will determine the response of the ensemble. Such couplings will impose that polymers have to relax in a cooperative manner, i.e., a monomer can only relax (change position) if some (or all) neighboring monomers perform simultaneously an appropriate movement. Because of such cooperative behavior,64–66 relaxations may be frustrated and the lifetime of meta-stable states may become exceedingly long, assuring a long-term memory of the action, which has established the meta-stable state in first place. Allowing for relaxations (e.g., by annealing or aging the sample), the initial changes on the way toward equilibrium may follow the steepest gradient in free energy (direction of the highest force). The system is trying to get to equilibrium as rapidly as it can, subject to whatever restraints are preventing this.67 However, for regions of different conformational states coexisting along the chains, it is not obvious if paths following the steepest gradient allow reaching equilibrium within accessible experimental timescales. Instead, more often than not, various experimental conditions and processing approaches lead to long-living meta-stable states of only partially equilibrated chains. The lifetimes of these meta-stable states depend on parameters characterizing the conditions under which the sample was prepared and the conditions under which the polymers attempted to equilibrate.68 Depending on the degree of correlations and the required cooperative movements for enabling relaxations toward equilibrium, for one and the same polymer, these lifetimes of meta-stable states may differ by many orders of magnitude. Thus, correlations of conformational states may decay very slowly, sometimes in a non-monotonic and a non-exponential fashion.26–29,69
A key challenge is thus to identify appropriate order parameters that are able to describe above observations, especially with respect to heterogeneities on various length- and timescales. In addition, appropriate parameters need to be defined, which can capture correlations between polymers and the corresponding cooperative movements of coupled polymers. It is not obvious if these parameters should be based on characteristic features averaged over all molecules or if we have to distinguish between “master” and “slaved” polymers. The first ones may be initiating a certain behavior, while the latter ones may serve as a reservoir of molecules that are “guided” by the first ones. In order to develop appropriate descriptions, we may possibly borrow from theoretical concepts existing in the context of non-equilibrium thermodynamics and related areas.
Possible measures for categorizing heterogeneities, meta-stable states, and the memorizing capacity of polymers may be based on the degree of deviation of the statistical distribution of chain conformations from a Gaussian distribution of the end-to-end vector. Such deviations may be quantified through parameters such as kurtosis (measure of the “tailedness,” given by the fourth moment of the distribution)70 or skewness (measure of the asymmetry of the probability distribution).71 Other potential measures may reflect spatial and temporal variations in the number of interpenetrating chains (“fluctuations” in entanglement density) or the length-scales and characteristic timescales of domains with distinguishable differences in density or segment orientation. Furthermore, for samples with macroscopically anisotropic chain orientation (preferred orientation) like in sheared samples, relaxation processes may depend on the orientation of the sample. In addition to mean values averaged over all chains, we may need to introduce parameters that account properly for the possibly dominating influence of a few highly deformed chains (like in a “shish”) on the resulting morphology of the whole sample.
In summary, observing forces (residual stresses) acting on polymer chain segments implies inevitably the existence of (some) correlations between polymer segments. Correlated segments often can relax only via cooperative (simultaneous) movements. Cooperativity, in turn, causes a slowing down of relaxations, introducing extremely long lifetimes of the corresponding meta-stable conformational states representing the memory of the polymer.
IV. CONCLUDING REMARKS
Memory and equilibrium are two incompatible terms. Only out-of-equilibrium systems can exhibit features that we typically attribute to systems possessing a memory: responsiveness and adaptability, including possibilities of learning. In this context, polymers can realize a tremendous number of non-equilibrium conformational states together with a high transformation ability that open up immense capacities for responding and adapting to changes. In addition, in contrast to non-interacting (“ideal”) polymer chains in equilibrium, which are uncorrelated and not affected by neighboring chains, non-equilibrated chains may be partially aligned and, thus, correlated. Consequently, we may anticipate a cooperative behavior implying constrained and very slow relaxations, providing a means for generating long-term memory effects.
Some may consider variability and changeability of properties as detrimental for applications where a well-defined (constant), predictable, and unique behavior of a polymer material is requested for the whole lifetime of the material.72 However, on the positive side, being able to generate meta-stable states on demand, which have extremely long relaxation times (longer than, say, 100 years), may provide polymer materials with sometimes superior properties that are stable for their whole service life. Depending on the kinds of desired properties requested by a particular application, we may transform a soft polymer into a hard one, a stiff polymer into an easily deformable one, an inert polymer into a responsive one, and an insulating polymer into a conductive one by choosing appropriate processing conditions.
Meta-stable conformational states can be generated through appropriate processing routes, i.e., at rates faster than the relevant inverse equilibrium relaxation time. If the resulting meta-stable states relax slowly, one may expect that continued processing like shearing might result in conformational states that are getting progressively further away from equilibrium. Thus, prolonged shearing or additional processing steps may amplify changes in properties. In such a case, we may expect that besides the processing rate, also the duration of the processing step will be of significance. For example, both the shear rate and the duration of shear73 affect crystallization of sheared polymer melts. So far, we have explored only a very small set of possible novel phenomena that result from polymer systems brought to states far-from-equilibrium. We have not addressed many fundamental questions: For example, are there limits for how far from equilibrium polymer systems can exist? What are the properties of ultimate non-equilibrium conformational states?
Thus, considering the full spectrum of options for tuning properties of polymers over many orders of magnitude, I anticipate that polymer science is at the beginning of an interesting era. Provided we decode the relations between properties and meta-stable conformational states, we may be able to accomplish polymer products with a desired property, which we can control by switching-on or switching-off suitable conformational states through appropriate processing steps.72 Thus, a profound understanding of out-of-equilibrium polymer properties and their adjustability will open the door to a bright future for polymer science.
I am very grateful for all the inspiring and fruitful discussions with Jörg Baschnagel, Sivarunder Chandran, Wenbing Hu, Greg McKenna, Murugappan Muthukumar, Simone Napolitano, Alexander Semenov, Jens-Uwe Sommer, Thomas Thurn-Albrecht, and Jun Xu as well as all members of the International Research Training Group (IRTG-1642)—Soft Matter Science. This work was financially supported by the Deutsche Forschungsgemeinschaft (DFG) via Project No. RE2273/18-1 and the IRTG.
Polymers span a large range in size, starting from the most compact form of a fully collapsed polymer globule up to a maximum length of the fully extended polymer chain. Thus, in contrast to atoms or small molecules, the “shape” of a polymer can and does vary largely in time and space. For example, the size of a single polymer chain consisting of 106 monomers of size b can vary from a diameter of 100 b for a collapsed compact globule to a mean end-to-end vector of length 1000 b for an equilibrium coil to a maximum length of 1 000 000 b for the fully extended chain, i.e., values varying by four (!) orders of magnitude. The corresponding conformational entropy of this chain can vary between a minimum value of 1 (for the fully extended chain), a maximum value for the equilibrium coil, and a much smaller number for the completely collapsed chain.
When the influence of external forces acting on a polymer melt stops, a plethora of relaxation processes, active on various length- and timescales, will try to remove these processing-induced meta-stable states, leading eventually to equilibrated polymers with a completely erased memory.
An experiment will not be able to distinguish a meta-stable state of finite lifetime but longer than the experimental timescale from the equilibrium state of lowest energy, which is the only “absolutely stable” state with an infinite lifetime.
The lifetime of memories related to deviations from equilibrium is never truly infinite. Some memories may have rather long lifetimes, of ten longer than the service life (life cycle) of the material, while some memories may fade away in rather short times, sometimes too short to be captured experimentally. Thus, polymer properties are not only related to the memory generated and stored at some past instant but depend also on events during the time-span between generation and retrieval of stored information, i.e., the “waiting time.” The degree of partial equilibration depends on how long the system was allowed to relax. In addition, depending on how far off-equilibrium the system was at the beginning of the “waiting process,” different partially equilibrated states may be reached after the same “waiting time.”
The lifetime of a memory (represented by specific material properties controlling future actions of the material) may be programmable or tuned. To this end, we need to understand fundamental mechanisms of encoding information and, in addition, the physical processes responsible for the “aging” of materials.