Polyelectrolyte complex characterization with isothermal titration calorimetry and colloid titration

Entropy Drives Interpolymer Association in Water: Insights into Molecular Mechanisms

Interpolymer association in aqueous solutions is essential for many industrial processes, new materials design, and the biochemistry of life. However, our understanding of the association mechanism is limited. Classical theories do not provide molecular details, creating a need for detailed mechanistic insights. This work consolidates previous literature with complementary isothermal titration calorimetry (ITC) measurements and molecular dynamics (MD) simulations to investigate molecular mechanisms to provide such insights. The large body of ITC data shows that intermolecular bonds, such as ionic or hydrogen bonds, cannot drive association. Instead, polymer association is entropy-driven due to the reorganization of water and ions. We propose a unifying entropy-driven association mechanism by generalizing previously suggested polyion association principles to include nonionic polymers, here termed polydipoles. In this mechanism, complementary charge densities of the polymers are the common denominators of association, for both polyions and polydipoles. The association of the polymers results mainly from two processes: charge exchange and amphiphilic association. MD simulations indicate that the amphiphilic assembly alone is enough for the initial association. Our proposed mechanism is a step toward a molecular understanding of the formation of complexes between synthetic and biological polymers under ambient or biological conditions.

Complexation between chitosan and carboxymethyl cellulose in weakly acidic, neutral, and weakly alcaline media

The interaction between carboxymethyl cellulose and partially reacetylated chitosan soluble in acidic and alkaline aqueous media is studied by light scattering and isothermal titration calorimetry in a wide pH range. It is shown that the formation of polyelectrolyte complexes (PEC) can occur in the pH range of 6-8, while this pair of polyelectrolytes loses the ability to complexation upon transition to a more alkaline medium. The revealed dependence of the observed enthalpy of interaction on the ionization enthalpy of the buffer indicates the participation of proton transfer from the buffer substance to chitosan and its additional ionization in the binding process. This phenomenon is first observed in a mixture of a weak polybase chitosan and a weak polyacid. The possibility to obtain soluble nonstoichiometric PEC by a direct mixing of the components in a weakly alkaline medium is shown. The resulting PECs are polymolecular particles in shape close to homogeneous spheres with a radius of about 100 nm. The obtained results are promising for creating of biocompatible and biodegradable drug delivery systems.

Driving force and pathway in polyelectrolyte complex coacervation

There is notable discrepancy between experiments and coarse-grained model studies regarding the thermodynamic driving force in polyelectrolyte complex coacervation: experiments find the free energy change to be dominated by entropy, while simulations using coarse-grained models with implicit solvent usually report a large, even dominant energetic contribution in systems with weak to intermediate electrostatic strength. Here, using coarse-grained, implicit-solvent molecular dynamics simulation combined with thermodynamic analysis, we study the potential of mean force (PMF) in the two key stages on the coacervation pathway for symmetric polyelectrolyte mixtures: polycation-polyanion complexation and polyion pair-pair condensation. We show that the temperature dependence in the dielectric constant of water gives rise to a substantial entropic contribution in the electrostatic interaction. By accounting for this electrostatic entropy, which is due to solvent reorganization, we find that under common conditions (monovalent ions, room temperature) for aqueous systems, both stages are strongly entropy-driven with negligible or even unfavorable energetic contributions, consistent with experimental results. Furthermore, for weak to intermediate electrostatic strengths, this electrostatic entropy, rather than the counterion-release entropy, is the primary entropy contribution. From the calculated PMF, we find that the supernatant phase consists predominantly of polyion pairs with vanishingly small concentration of bare polyelectrolytes, and we provide an estimate of the spinodal of the supernatant phase. Finally, we show that prior to contact, two neutral polyion pairs weakly attract each other by mutually induced polarization, providing the initial driving force for the fusion of the pairs.

Effectively remove p-arsanilic acid from water over amphiphilic amino modified collagen fiber

Efficient and rapid removal of p-arsanilic acid (p-ASA) in water is very important in environmental protection and human health, however it is still a severe challenge in actual engineering. Herein, a novel sorbent (CF-PEI) was successfully fabricated by simply modifying the amphiphilic skin collagen fiber (CF) substrate with Polyethylenimine (PEI). The as-prepared CF-PEI exhibits high-efficiency adsorption for negatively charged p-ASA with aromatic rings due to the introduction of amino groups and the existence of hydrophobic bands, and the maximum adsorption capacity of CF-PEI for p-ASA was high up to 285.71 mg g^-1. In addition, the adsorption mechanism of CF-PEI on p-ASA mainly includes electrostatic interaction, hydrogen bond and amphiphilicity. The multi-level all-fiber structure of CF makes it mainly focus on surface mass transfer with short mass transfer distance, and its capillary drainage effect can realize large flow and rapid separation. CF-PEI based on CF can realize the ability to separate low-concentration p-ASA with high flow rate and high efficiency. The effective processing volume was 12.5 L g^-1 when the separation flux reached as high as 9931.27 L m^-2 h^-1. Notably, the p-ASA adsorbed on CF-PEI was almost completely eluted by NaOH (0.5 mol L^-1). The adsorbent is convenient to prepare, recyclable, high in efficiency, and has a great application prospect in removing organic micro-pollutants.

Associative structures formed from cellulose nanofibrils and nanochitins are pH-responsive and exhibit tunable rheology

HYPOTHESIS

Nanocellulose and nanochitin are both biobased materials with complementary structures and properties. Both exhibit pH-dependent surface charges which are opposite in sign. Hence, it should be possible to manipulate them to form complexed structures via ionic bond formation at prescribed pH conditions.

EXPERIMENT

Nanocellulose and nanochitin were mixed after exposure to acidic or neutral conditions to influence their ionization state. The heat of interaction during the introduction of nanochitin to nanocellulose was monitored via isothermal titration calorimetry. The strength and gel properties of the resulting structures were characterized via rheological measurement.

FINDINGS

The resultant gel properties in the designed hybrid systems were found to depend directly on the charge state of the starting materials, which was dictated by pH adjustment. Different interparticle interactions including ionic attraction, hydrophobic associations, and physical entanglement were identified in the systems and the influence of each was elucidated for different conditions of pH, concentration, and ratio of nanochitin to nanocellulose. Hydrophobic associations between neutralized nanochitin particles were found to contribute strongly to increased elastic modulus values. Ionic complex formation was found to provide enhanced stability under broader pH conditions, while physical entanglement of cellulose nanofibers was a substantial thickening mechanism in all systems.

Lower Critical Solution Temperature-Driven Self-Coacervation of Nonionic Polyester Underwater Adhesives

To enable attachment to underwater surfaces, aquatic fauna such as mussels and sandcastle worms utilize the advantages of coacervation to deliver concentrated protein-rich adhesive cocktails in an aqueous environment onto underwater surfaces. Recently, a mussel adhesive protein Mfp-3s, was shown to exhibit a coacervation-based adhesion mechanism. Current synthetic strategies to mimic Mfp-3s often involve complexation of oppositely charged polymers. Such complex coacervates are more sensitive to changes in pH and salt, thereby limiting their utility to narrow ranges of pH and ionic strength. In this study, by taking advantage of the lower critical solution temperature-driven coacervation, we have created mussel foot protein-inspired, tropoelastin-like, bioabsorbable, nonionic, self-coacervating polyesters for the delivery of photo-cross-linkable adhesives underwater and to overcome the challenges of adhesion in wet or underwater environments. We describe the rationale for their design and the underwater adhesive properties of these nonionic adhesives. Compared to previously reported coacervate adhesives, these "charge-free" polyesters coacervate in wide ranges of pH (3-12) and ionic strength (0-1 M NaCl) and rapidly (<300 s) adhere to substrates submerged underwater. The study introduces smart materials that mimic the self-coacervation and environmental stability of Mfp-3s and demonstrate the potential for biological adhesive applications where high water content, salts, and pH changes can be expected.

Recent progress in the science of complex coacervation

Complex coacervation is an associative, liquid-liquid phase separation that can occur in solutions of oppositely-charged macromolecular species, such as proteins, polymers, and colloids. This process results in a coacervate phase, which is a dense mix of the oppositely-charged components, and a supernatant phase, which is primarily devoid of these same species. First observed almost a century ago, coacervates have since found relevance in a wide range of applications; they are used in personal care and food products, cutting edge biotechnology, and as a motif for materials design and self-assembly. There has recently been a renaissance in our understanding of this important class of material phenomena, bringing the science of coacervation to the forefront of polymer and colloid science, biophysics, and industrial materials design. In this review, we describe the emergence of a number of these new research directions, specifically in the context of polymer-polymer complex coacervates, which are inspired by a number of key physical and chemical insights and driven by a diverse range of experimental, theoretical, and computational approaches.

Contrasting Assemblies of Oppositely Charged Proteins

Oppositely charged proteins can form soluble assemblies that under specific physical chemical conditions lead to liquid-liquid phase separation, also called heteroprotein coacervation. Increasing evidence suggests that surface charge anisotropy plays a key role in heteroprotein complexation, and coacervation. Here, we investigated complexation of an acidic protein, β-lactoglobulin (BLG), with two basic proteins, rapeseed napin (NAP) and lysozyme (LYS), of similar net charge and size but differing in surface charge distribution. Using turbidity measurements and isothermal titration calorimetry, we confirmed that LYS binds BLG as expected from previous studies. This interaction leads to two types of phase separation phenomena, depending on pH: liquid-solid phase separation in the case of strong electrostatic attraction and liquid-liquid phase separation for weaker attraction. More interestingly, we showed using dynamic light scattering that NAP interacts with BLG, resulting in formation of assemblies in the nanometer size range. The formation of assemblies was also evident when modeling the interactions using Brownian dynamics for both BLG + NAP and BLG + LYS. Similarly, to DLS, BLG and NAP formed smaller assemblies than BLG with LYS. The molecular details rather than the net charge of BLG and NAP may therefore play a role in their assembly. Furthermore, simulated BLG + NAP assemblies were larger than those experimentally detected by DLS. We discuss the discrepancy between experiments and simulations in relation to the limitations of modelling precisely the molecular characteristics of proteins.

Effects of Chain Length of Chitosan Oligosaccharides on Solution Properties and Complexation with siRNA

In the context of gene delivery, chitosan has been widely used as a safe and effective polycation to complex DNA, RNA and more recently, siRNA. However, much less attention has been paid to chitosan oligosaccharides (COS) despite their biological properties. This study proposed to carry out a physicochemical study of COS varying in degree of polymerization (DP) from 5 to 50, both from the point of view of the solution properties and the complexing behavior with siRNA. The main parameters studied as a function of DP were the apparent pKa, the solubility versus pH, the binding affinity with siRNA and the colloidal properties of complexes. Some parameters, like the pKa or the binding enthalpy with siRNA, showed a marked transition from DP 5 to DP 13, suggesting that electrostatic properties of COS vary considerably in this range of DP. The colloidal properties of siRNA/COS complexes were affected in a different way by the COS chain length. In particular, COS of relatively high DP (≥50) were required to form small complex particles with good stability.

Immobilization of β-galactosidase by complexation: Effect of interaction on the properties of the enzyme

In the present work, we aimed to explore the molecular binding between alginate and β-galactosidase, as well as the effect of this interaction on the activity retention, thermal stability, and kinetic properties of the enzyme. The impact of pH and enzyme/alginate ratio on physicochemical properties (turbidity, morphology, particle size distribution, ζ-potential, FTIR, and isothermal titration calorimetry) was also evaluated. The ratio of biopolymers and pH of the system directly affected the critical pH of complex formation; however, a low alginate concentration (0.1 wt%) could achieve an electrical charge equivalence at pH 3.4 with 93.72% of yield. The binding between β-galactosidase and alginate was an equilibrium between enthalpic and entropic contributions, which promoted changes in the structure of the enzyme. Nevertheless, this conformational modification was reversible after the dissociation of the complex, which allowed the enzyme to regain its activity. These findings will likely broaden functional applications of enzyme immobilization.

Biorelated Polyelectrolyte Coatings Studied by in Situ Attenuated Total Reflection-Fourier Transform Infrared Spectroscopy: Deposition Concepts, Wet Adhesiveness, and Biomedical Applications

In this conceptual contribution, thin functional coatings consisting of either pure polyelectrolytes (PELs) or complexes between oppositely charged PELs at model and applied substrates are outlined. Latter PEL/PEL complexes were deposited by two concepts. In a first well-known concept, PEL multilayers (PEM) were consecutively deposited according to the layer-by-layer (LbL) technique. In a second less known concept, PEL complex (PEC) nanoparticles (NPs) preformed by mixing polycation (PC) and polyanion (PA) solutions were deposited in one step. Both concepts based on binary oppositely charged PELs are compared to one based on a single polycation system. Examples shall be given on adhesiveness, nanostructure, and biomedical applications of PEM and PEC NP coatings. In situ attenuated total reflection (ATR) infrared (IR) spectroscopy, circular dichroism (CD), and scanning force microscopy (SFM) were used for molecular, optical, and microscopic characterization. At first, results on the adsorbed amount and wet adhesiveness of pure (single-component) PEL coatings as a function of charge density are given to motivate coatings of mixed oppositely charged PELs. Second, the wet adhesiveness of PEM and PEC NP coatings of identical PEL compounds in aqueous media varying the molar charge ratio ( n-/ n+) and the deposition step z, respectively, is compared. Upon comparing the three PEL deposition concepts, it is suggested that the lack or absence of excess charge at the PEL/surface interface is one of the main factors for the wet adhesiveness of all pure PEL, PEM, and PEC NP coatings. Finally, the potential of PEM and PEC NP coatings for biomedical applications is outlined. Concerning biopassivation, PEM coatings excessed or terminated by PA repel proteins with low isoelectric points. Concerning bioactivation, PEM coatings loaded with antibiotics as well as PEC NP coatings loaded with therapeutic bisphosphonates showed retarded, optionally temperature responsive drug release for applications in acute surgery and bone healing, and immunoglobulin/PEL complex coatings might open theranostic applications.

Influence of different classes of crosslinkers on alginate polyelectrolyte nanoparticle formation, thermodynamics and characteristics

Complexation of linear alginate polyanions with different classes of crosslinkers (divalent cations, polycations, positively charged surfactants) was investigated, to unravel their effects on nanoparticle formation. The goal was to define the crosslinker-to-alginate molar ratios at which nanoparticles are formed, and to reveal the underlying thermodynamics and molecular interactions using dynamic and electrophoretic light scattering, isothermal titration calorimetry, and infrared spectroscopy. Alginate nanoparticles were formed across a limited range of molar ratios that was specific for each crosslinker, and had different size and stability. Thermodynamic parameters of alginate complexation with crosslinkers showed that nanoparticle formation was in all cases entropy driven, together with a minor enthalpic contribution. The crosslinking mechanism was based on ionic interactions, with accompanying weaker interactions specific for each crosslinker, and involved characteristic macroscopic association constants (K_a1) for complexation of alginate (range, 10⁴-10⁹M^-1). Additionally, the ionic strengths of the media influenced the characteristics and stabilities of the polyelectrolyte nanoparticles.

Modelling and predicting the interactions between oppositely and variously charged polyelectrolytes by frontal analysis continuous capillary electrophoresis

In this work, a systematic study of the interactions between poly(l-lysine) and variously charged statistical copolymers of acrylamide and 2-acrylamido-2-methyl-1-propanesulfonate (PAMAMPS) has been carried out by frontal analysis continuous capillary electrophoresis (FACCE). FACCE was successfully implemented to obtain the interaction parameters (binding constant and stoichiometry) at different ionic strengths and for different PAMAMPS charge densities varying between 15% and 100%. The range of investigated ionic strengths was carefully adjusted according to the PAMAMPS charge density to obtain measurable binding constants by FACCE (i.e. formation binding constant typically comprised between 10⁴ and 10⁶ M^-1). The number of released counter-ions during the polyelectrolyte complex formation was systematically quantified via the ionic strength dependence of the binding constant and was compared to the total condensed counter-ion reservoir according to Manning theory on counter-ion condensation. A descriptive and predictive model relating the physico-chemical properties of the two partners, the binding constant and the ionic strength is proposed in the framework of multiple independent interaction sites of equal energy.

Thermodynamics of Ion Pair Formations Between Charged Poly(Amino Acid)s

Electrostatic interactions between the positively and negatively charged amino acids in proteins play an important role in macromolecular stability, binding, and recognition. Numerous amino acids in proteins are ionizable and may exist in negatively (e.g., Glu, Asp, Cys, Tyr) or positively (e.g., Arg, Lys, His, Orn) charged form dependent on pH and their pKas. In this work, isothermal titration calorimetry was used to determine the average standard values of thermodynamic parameters (the Gibbs free energy, enthalpy, entropy, and the heat capacity) of interaction between the positively charged amino acid homopolymers (polyarginine, polylysine, and polyornithine) and the negatively charged homopolymers (polyaspartic and polyglutamic acids). These values are of potential use in the computational models of interacting proteins and other biological macromolecules. The study showed that oppositely charged poly(amino acid)s bound each other with the stoichiometry of one positive to one negative charge. Arginine bound to the negatively charged amino acids with exothermic enthalpy and higher affinity than lysine. This result also suggests that positive charges in proteins should not be considered entirely equivalent if carried by lysine or arginine. The difference in binding energy of arginine and lysine association with the negatively charged amino acids was attributed to the enthalpy of the second ionic hydrogen bond formation between the guanidine and carboxylic groups. Despite the favorable enthalpic contribution, all such ion pair formation reactions were largely entropy-driven. Consistent with previously observed ionic interactions, the positive heat capacity was always observed during the amino acid ion pair formation.

Charge heterogeneity induced binding and phase stability in β-lacto-globulin–gelatin B gels and coacervates at their common pI

An understanding of the interactions between gelatin B (GB) and β-lacto-globulin (β-Lg) mainly arising from surface selective patch binding occurring at their common pI (≈5.0 ± 0.5) in the absence of added salt.

Complexation between polyallylammonium cations and polystyrenesulfonate anions: the effect of ionic strength and the electrolyte type

Complexation between polyallylammonium cations and polystyrenesulfonate anions was investigated in aqueous solutions of binary 1 : 1 sodium electrolytes (NaX, X = F, Cl, Br, I, NO3, ClO4) by means of microcalorimetry, dynamic light scattering, electrokinetics and spectrophotometry. At lower molar ratios of monomer units charged polyelectrolyte complexes were formed. At molar ratios close to equivalence and at lower salt concentrations (c(NAX)/mol dm(-3) ≤ 0.1) flocculation occurred. The obtained precipitates contained approximately equimolar amounts of oppositely charged monomer units. At c(NAX)/mol dm(-3) ≥ 0.5 (X = NO3, ClO4) and in the case when the polycation was present in excess, the amount of positively charged monomer units in the precipitate was higher than that of negatively charged monomers (asymmetric neutralisation). In addition, the aggregation of positively charged complexes in concentrated solutions of all investigated electrolytes was noticed. The onset of aggregation was strongly anion specific. However, the aggregation of negatively charged complexes did not occur even at c(NaX) = 3 mol dm(-3). The composition of the insoluble products at equimolar ratio of monomer units and higher concentrations of NaNO3 and NaClO4 was dependent on the order of addition, indicating non-equilibrium interpolyelectrolyte neutralisation under all ionic conditions. At 25 °C and c(NaClO4) = 1 mol dm(-3) equilibrium was not reached after two months. In contrast, the supernatants showed no traces of free polyanion chains after being heated for a week at 60 °C. The pairing of monomer units was predominantly entropically driven, irrespective of the type of reaction products formed (polyelectrolyte complexes, precipitates) and the electrolyte type. The results obtained indicate that the overcharging is not an enthalpically demanding process. The calorimetric measurements also suggest that the strong influence of counteranions on the composition of the reaction product must be related to differences in ion distribution around polycations. However, despite rather similar energetics for complex and precipitate formation in the presence of various sodium salts a clear correlation of formation enthalpies with corresponding anion hydration enthalpies (Hofmeister series) was observed. Somewhat surprisingly, the titration calorimetry experiments have also revealed that the increase in electrolyte concentration affects the enthalpy of interpolyelectrolyte neutralisation negligibly.

Determining the colloidal behavior of ionically cross-linked polyelectrolytes with isothermal titration calorimetry

Mixtures of polyelectrolytes and multivalent counterions can self-assemble into colloidal complexes. These complexes attract widespread interest in applications such as medicine, household product formulations, and separation processes. To facilitate the development of these colloidal dispersions, we examined isothermal titration calorimetry (ITC) as an automated screening tool for identifying the polymer and multivalent counterion compositions that (1) form ionically cross-linked colloidal complexes and (2) lead to their rapid coagulation (and macroscopic phase separation). By studying various polyelectrolyte/multivalent counterion mixtures, we have identified and generalized the features in the ITC data that indicate colloidal complex formation and coagulation. The limitations of this calorimetric screening method were also elucidated. These analyses suggest that ITC can be effective for screening the short-term colloidal behavior of polyelectrolyte/multivalent counterion mixtures but are unreliable in revealing their long-term (equilibrium) properties.

Thermodynamic characterization of polypeptide complex coacervation

The interactions between a series of oppositely charged polypeptide pairs are probed using isothermal titration calorimetry (ITC) in combination with turbidity measurements and optical microscopy. Polypeptide complex coacervation is described as a sequence of two distinct binding steps using an empirical extension of a simple ITC binding model. The first step consists of the formation of soluble complexes from oppositely charged polypeptides (ion pairing), which in turn aggregate into insoluble interpolymer complexes in the second step (complex coacervation). Polypeptides have identical backbones and differ only in their charged side groups, making them attractive model systems for this work. The poly(l-ornithine hydrobromide) (PO)/poly(l-glutamic acid sodium salt) (PGlu) system is used to examine the effects of parameters such as the salt concentration, pH, temperature, degree of polymerization, and total polymer concentration on the thermodynamic characteristics of complexation. Complex coacervation in all probed systems is found to be endothermic, essentially an entropy-driven processes. Increasing the screening effect of the salt on the polyelectrolyte charges diminishes their propensity to interact, leading to a decrease in the observed energy change and coacervate quantity. The pH plays an important role in complex formation through its effect on the degree of ionization of the functional groups. Plotting the change in enthalpy with temperature allows the calculation of the heat capacity change (ΔC(p)) for the PO/PGlu interactions. Finally, ITC revealed that complex coacervation is promoted when higher total polymer concentrations or polypeptide chain lengths are used.

Complexation and coacervation of polyelectrolytes with oppositely charged colloids

Polyelectrolyte-colloid coacervation could be viewed as a sub-category of complex coacervation, but is unique in (1) retaining the structure and properties of the colloid, and (2) reducing the heterogeneity and configurational complexity of polyelectrolyte-polyelectrolyte (PE-PE) systems. Interest in protein-polyelectrolyte coacervates arises from preservation of biofunctionality; in addition, the geometric and charge isotropy of micelles allows for better comparison with theory, taking into account the central role of colloid charge density. In the context of these two systems, we describe critical conditions for complex formation and for coacervation with regard to colloid and polyelectrolyte charge densities, ionic strength, PE molecular weight (MW), and stoichiometry; and effects of temperature and shear, which are unique to the PE-micelle systems. The coacervation process is discussed in terms of theoretical treatments and models, as supported by experimental findings. We point out how soluble aggregates, subject to various equilibria and disproportionation effects, can self-assemble leading to heterogeneity in macroscopically homogeneous coacervates, on multiple length scales.

Dynamic aspects of films prepared by a sequential deposition of species: perspectives for smart and responsive materials

The deposition of surface coatings using a step-by-step approach from mutually interacting species allows the fabrication of so called "multilayered films". These coatings are very versatile and easy to produce in environmentally friendly conditions, mostly from aqueous solution. They find more and more applications in many hot topic areas, such as in biomaterials and nanoelectronics but also in stimuli-responsive films. We aim to review the most recent developments in such stimuli-responsive coatings based on layer-by-layer (LBL) depositions in relationship to the properties of these coatings. The most investigated stimuli are based on changes in ionic strength, temperature, exposure to light, and mechanical forces. The possibility to induce a transition from linear to exponential growth in thickness and to change the charge compensation from "intrinsic" to "extrinsic" by controlling parameters such as temperature, pH, and ionic strength are the ways to confer their responsiveness to the films. Chemical post-modifications also allow to significantly modify the film properties.

Isothermal microcalorimetry to investigate non specific interactions in biophysical chemistry

Isothermal titration microcalorimetry (ITC) is mostly used to investigate the thermodynamics of “specific” host-guest interactions in biology as well as in supramolecular chemistry. The aim of this review is to demonstrate that ITC can also provide useful information about non-specific interactions, like electrostatic or hydrophobic interactions. More attention will be given in the use of ITC to investigate polyelectrolyte-polyelectrolyte (in particular DNA-polycation), polyelectrolyte-protein as well as protein-lipid interactions. We will emphasize that in most cases these “non specific” interactions, as their definition will indicate, are favoured or even driven by an increase in the entropy of the system. The origin of this entropy increase will be discussed for some particular systems. We will also show that in many cases entropy-enthalpy compensation phenomena occur.