Theory of swelling of a crosslinked substance in equilibrium with a pure solvent in various phases. Part II: The variation of the pressure

A theory of swelling is presented which describes the equilibrium swelling of a body in a solvent in its various states. The pressure dependence of the pressure-concentration swelling curves is treated for the swelling agent occurring in the liquid, crystalline or vapor phase. The slopes of the pressureconcentration swelling curves are dependent on the differential volume of dilution of the solvent and, additionally, on the volume changes of vaporization, crystallization, and sublimation of the solvent corresponding to the state of the swelling agent. At the melting and boiling pressure of the swelling agent the swelling curves change their slopes with a discontinuity, which is most distinct at the evaporation transition. By measurements of the slopes of the swelling curves at the transition pressure the derivative ₁/w₁ at constant temperature and pressure, which is the change of the chemical potential of the solvent with its weight fraction, is obtained. Thus, a further equation is given to test statistical theories at the transition pressures. Simultaneous variations of the swelling with changes of temperature are also treated.     

Swelling equilibria and volume phase transition of polyelectrolyte gel with strongly dissociated groups

The peculiarities of the swelling equilibrium and volume phase transition of polyelectrolyte copolymer gels consisting of acrylamide and 2-acrylamido-2-methyl-1-propane sulphonic acid (AAm/AMPS) have been studied as a function of copolymer composition and gel structure. Equilibrium swelling for AAm/AMPS gels in buffer solutions, pure water and aqueous salt (NaCl) solutions were investigated. The swelling curves were calculated using the Hasa–Ilavský–Dušek theory and obtained experimentally. The agreement is reasonably good, and the HID theory can be used to estimate the swelling and structural parameter of AAm/AMPS gels. The volume phase transition has been generated by changing the solvent composition by progressive substitution of water by acetone. The critical interaction parameter corresponding to collapse depends strongly on the composition of the gel, since the extent of collapse is determined by composition and cross-link density of the gel.     

Tricritical point induced by smectic ordering of a nematic gel

The authors study volume phase transitions of a nematic gel immersed in a liquid crystal (LC) solvent, which shows a second-order nematic-smectic A phase transition (NST). Combining Flory's elastic energy [Principles of Polymer Chemistry (Cornell University Press, Ithaca, 1953)] for a swelling of the gel with the McMillan model [Phys. Rev. A 4, 1238 (1971)] for smectic ordering, the authors calculate the equilibrium swelling of the gel and smectic order parameters as a function of temperature. The authors take into account an attractive interaction parameter c between the gel and LC solvents. On increasing the value of the coupling constant c, a second-order NST of the gel is changed to a first-order one and a continuous volume phase transition of the gel is changed to a discontinuous one. The authors find a tricritical point of the gel induced by smectic ordering.     

Specific swelling behaviors of alkali‐metal poly(styrene sulfonate) gels in aqueous solvent mixtures

Counterion‐ and solvent‐specific swelling behaviors were investigated for alkali‐metal poly(styrene sulfonate) (PSSM) gels having different degrees of sulfonation in aqueous organic solvent mixtures [water plus methanol, ethanol, 2‐propyl alcohol, t‐butyl alcohol, dimethyl sulfoxide (DMSO), acetone, acetonitrile, tetrahydrofuran, or dioxane]. With an increasing organic solvent concentration, most gel systems, except for DMSO, showed a volume phase transition. The transition abruptly occurred without significant deswelling in the lower solvent concentration region. Such swelling behavior contrasted with that of other common charged gel systems, including alkali‐metal polyacrylate (PAAM) gels, which showed gel collapse after gradual deswelling with an increasing organic solvent concentration. The dielectric constant at the critical transition point (D_cr) for most mixed solvent systems decreased in the order of PSSK ≥ PSSCs ≥ PSSNa > PSSLi; that is, larger counterion systems were favorable for the transition. The counterion specificity also contrasted with our previous results for PAAM gels: PAANa > PAAK > PAALi ～ PAACs. On the other hand, the solvent specificity for the PSSM gels was similar to that for the PAAM gels; the higher the dielectric constant was of the organic solvent, the higher the D_cr value was at which the transition occurred. These specificities were examined on the basis of the solvation properties of the counterions and polymer charged groups and the solvent properties such as the Gutmann–Mayer donor number and acceptor number. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1166–1175, 2007     

Theoretical analysis of sorption of a binary solvent in a polymer phase. II. Occurrence of maxima and minima in the curve of total sorption

It has been shown that sorption equilibrium in the system polymer–mixed solvent and the total sorption as one of its manifestations can be derived from osmotic equilibrium. The equilibrium relation for the dependence of the osmotic pressure II (as the potential for total sorption) on the composition of the ternary polymer-containing phase also includes the preferential sorption ε. This complication leads to difficulties in the analysis of the dependence of II on composition: for this reason, analysis has been limited to the case of a very dilute polymer phase. If preferential sorption is neglected, the occurrence of an extremum on the curve representing the dependence of the total sorption on the composition of the mixed solvent is affected by the Flory-Huggins parameters as in the occurrence of an inversion in preferential sorption, with the exception that in the former case the difference in the molar volumes of the solvent components contributes a term smaller by a factor of two. In the general case, however, the contribution of preferential sorption to the osmotic pressure (which has always a negative sign) also plays its role. Consequently, while total sorption, at a low preferential sorption and at a large positive value of the solvent–solvent interaction parameter χ₁₂, can exhibit a maximum, a larger preferential sorption can overcompensate the effect of the parameter χ₁₂, so that a minimum appears. The coexistence of a minimum with a maximum on the same curve is possible in some cases with positive χ₁₂. The latter theoretical predictions have not yet been confirmed experimentally. At a negative χ₁₂ the extremum is always a minimum.     

Emulsion stability based on phase behavior in sodium naphthenates containing systems: gels with a high organic solvent content

Addition of heptane to a sodium naphthenates/toluene/water system at 25 degrees C reduces the lamellar liquid-crystal phase range and increases the microemulsion phase range. Both of these effects result in the extension of the composition range where emulsions have low stability. This effect is even stronger at 40 degrees C. Heptane addition also results in the formation of very stable emulsions within the overlapping phase-existence ranges of aqueous (L1) and organic (L2) phases. Stable non-birefringent gel observed in equilibrium with L1 and L2 phases contains only a small percentage of water and sodium naphthenates. The swelling behavior of an unstable gel, an emulsion previously compressed by centrifugation, appears to be due to a stepwise thickening of the thin liquid films between the droplets.     

Swelling of poly(N-isopropylacrylamide) gels in water-aprotic solvent mixtures

The swelling volume of poly(N-isopropylacrylamide) (PIPAAm) gel in aprotic solvents (acetonitrile (AcN)-, tetrahydrofuran (THF)-, 1,4-dioxane (DO)- and dimethylsulfoxide (DMSO))-water mixtures was measured at 25°C. The gel swollen in water shrank first and then reswelled with addition of the aprotic solvents. At an intermediate mole fraction (XDMSO) range of DMSO-water mixtures, the gel demonstrated a reentrant swelling phenomenon the hydrated gel shrank first on addition of a small amount of solvent, showed a typical wide reentrant transition, and gradually reswelled in the range near pure solvent. On the other hand, the gels in AcN-, THF-, and DO-water mixtures demonstrated a reentrant-convex swelling phenomenon: the gels reswelled after a reentrant phase transition in low Xorg (XAcN, XTHF and XDO), showed a maximum swelling in the intermediate Xorg region, and shrank again gradually in the high Xorg region. Such a swelling behavior of the gel was interpreted by correlating with solution properties of the aqueous aprotic solvent mixtures.The strength of hydrogen bonding around amide groups of the homopolymer was examined in pure solvents (water, THF, and DMSO) and in all proportion of aqueous THF to observe the relation with swelling behavior of gel by spectrum analysis of the amide I and II bands of Fourier Transform Infrared Spectroscopy (FT-IR). The swelling properties of gels in solvents and the aqueous mixtures were well correlated with the peak shifts of amide groups of the homopolymer.     

Kinetics of styrene uptake by a polyurethane network during the formation of interpenetrating polymer networks

Due to insolubility of the components, formation of interpenetrating polymer networks (IPNs) requires particular ways of synthesis. Among others, IPNs can be prepared by the sequential technique where a network is swollen in a monomer and its crosslinker, which are then polymerized in situ. The simplest case is to swell at equilibrium; however this leads to IPNs of a given composition. For obtaining other compositions, swelling has to be stopped before equilibrium, or the swollen network (gel) has to be deswollen to a certain extent. Therefore, diffusivity of the monomer within the gel has to be known. The kinetics of monomer uptake was studied for a polyether urethane/styrene-divinylbenzene system which gives transparent materials despite the difference in refractive indexes. This allows direct visual observations of the monomer progress within the network. The results are not fully in agreement with the theories of Tanaka and of Candau which both predict the progression of a solvent in a polymeric gel. Two regimes of swelling depending on the concentration distribution of the monomer within the gel were found.     

Interlamellar forces and the thermodynamic characterization of lamellar phospholipid systems

In this review, we summarize a series of experimental studies of the swelling of zwitterionic lamellar phospholipid and phospholipid-cholesterol systems using a novel double twin calorimeter. With this method, one can obtain simultaneous measures of the partial molar free energy and the partial molar enthalpy, and the experimental studies thus provide a complete thermodynamic characterization of the isothermal swelling process. A major finding is that the swelling of lamellar zwitterionic phospholipid systems at higher water contents (> 4 water molecules per lipid) is endothermic. The enthalpy has the opposite sign relative to the free energy, thus demonstrating that the swelling process is entropy driven. The water uptake also triggers a transition from a gel to a liquid crystalline state showing that, at given water content, the swelling pressure is much higher in the liquid crystal than in the gel. When cholesterol is added to the system the liquid ordered phase is formed at all available water contents. In this phase the swelling pressure varies smoothly and takes relatively low values at water contents below two per phospholipid, while it is substantially higher than in the gel phase at higher water contents. Together, these data demonstrate that the swelling pressure is sensitive to the phase state of the lipids. We also describe a series of studies that demonstrate that the addition of a second polar solute to the phospholipid–water system has a remarkably small effect on the swelling behavior when analyzed with respect to solvent volume. The reviewed experimental studies provide a thermodynamic characterization of the swelling of lamellar zwitterionic phospholipid systems that should be encompassed in the mechanistic molecular interpretation of the “hydration force.”     

The effect of solvent composition on swelling and shrinking properties of poly(acrylamide-co-itaconic acid) hydrogels

The peculiarities of the equilibrium swelling ratio and swelling-shrinking kinetics of polyelectrolyte copolymeric hydrogels consisting of acrylamide and itaconic acid (AAm/IA) have been studied in water/nonsolvent (acetone, methanol, ethanol and 1-butanol) mixtures as a function of solvent composition and IA content in the hydrogel. The phase transition of these hydrogels was generated by changing the solvent composition by progressive substitution of water by the nonsolvent. For all P(AAm/IA) hydrogels, the form of the shrinking curves was determined to be strongly dependent on the type of the nonsolvent used. The rate of shrinking of these hydrogels increased in the order 1-butanol < ethanol < methanol < acetone.     

Oleophilic ion-exchange resins. IV. Swelling of quaternary ammonium polymers in mixed solvents

The swelling characteristics of an oleophilic anion-exchange resin in methanol–benzene and ethanol–chloroform mixed solvent systems were compared with those of a conventional anion-exchange resin. The oleophilic resin was prepared by amination of chloromethylated polystyrene 1% DVB with N,N-dimethyldodecylamine. It showed a large shift of the swelling peak from polar to less polar solution compositions in both methanol–benzene and ethanol–chloroform systems as compared with the swelling of conventional resins. Total solvent uptake and solvent distribution between resin and solvent phases were also determined. The less polar solvent (benzene or chloroform) was sorbed preferentially by the oleophilic resin over a wide range of composition, while preference for the more polar solvent (methanol or ethanol) by the conventional resin was shown over the entire composition of the mixed solvent systems. The Newman-Krigbaum treatment of mixed solvents was applied to swelling data on the ethanol–chloroform–oleophilic resin system, where the volume of the gel network plus the solvent imbibed was relatively constant over the entire range of composition. The result suggests a strong similarity of the liquid–liquid interaction terms in this gel phase compared with those in the pure binary liquid phase.     

Equilibrium phase behavior of the membrane forming water-DMSO-EVAL copolymer system

The equilibrium phase behavior of ethylene vinyl alcohol (EVAL) copolymer in mixtures of DMSO (dimethylsulfoxide, solvent) and water (nonsolvent) was studied for different temperatures. Both crystallization-induced gelation and liquid-liquid demixing were observed. From the determined phase diagram of this system at 25°C, three regions may be identified, i.e., a homogeneous region, a gel region, and binodal region in which both types of phase transition take place. At higher temperatures, crystallization isotherm was found to intersect the binodal phase boundary, which is analogous to the phase behavior reported by Stokes and Berghmans for several binary systems.     

Vitrification of polymer solutions as a function of solvent quality, analyzed via vapor pressures

Vapor pressures (headspace sampling in combination with gas chromatography) and glass transition temperatures [differential scanning calorimetry (DSC)] have been measured for solutions of polystyrene (PS) in either toluene (TL) (10-70 degrees C) or cyclohexane (CH) (32-60 degrees C) from moderately concentrated solutions up to the pure polymer. As long as the mixtures are liquid, the vapor pressure of TL (good solvent) is considerably lower than that of CH (theta solvent) under other identical conditions. These differences vanish upon the vitrification of the solutions. For TL the isothermal liquid-solid transition induced by an increase of polymer concentration takes place within a finite composition interval at constant vapor pressure; with CH this phenomenon is either absent or too insignificant to be detected. For PS solutions in TL the DSC traces look as usual, whereas these curves may become bimodal for solutions in CH. The implications of the vitrification of the polymer solutions for the determination of Flory-Huggins interaction parameters from vapor pressure data are discussed. A comparison of the results for TL/PS with recently published data on the same system demonstrates that the experimental method employed for the determination of vapor pressures plays an important role at high polymer concentrations and low temperatures.     

Theory of swelling of a crosslinked substance in equilibrium with a solvent in various phases

In this paper the thermodynamic theory of a body in a liquid, crystalline or vaporized solvent is treated. The equilibrium swelling curves are discussed for the different states of the solvent. The slopes of the swelling curves are dependent on the differential enthalpy of dilution of the solvent and, additionally, on the enthalpies of vaporization, crystallization and sublimation of the solvent related to the state of the swelling agent. The slopes of the swelling curves are determined by the differential heat of vaporization, the differential heat of solution of the solvent or the differential heat of fusion according to the state of the swelling agent. Directly below the melting pointT _m,1, or directly above the boiling pointT _b,1 of the solvent the swelling curves change their slopes with a sharp bend. This phenomenon can be used to determine (₁/w ₁) at constant temperature and pressure, which means the change of the chemical potential ₁, with the change of the weight fractionw ₁ of the solvent. Using a simplified statistical thermodynamic relation it is possible to describe the principal courses of the swelling curves in all states of the solvent.     

Phase equilibria in polymer/solvent systems VII swelling pressure and swelling equilibrium between gaseous or liquid phases and a gel in a multicomponent system

Differential equations for swelling pressure and swelling equilibria in two-phase systems consisting of many components have been derived. The result includes simple equilibria of gaseous or liquid solvent and a gel which are known from the literature.     

从溶胀平衡研究玻璃态高聚物的凝聚缠结网络

在13~15℃室温条件下对聚苯乙烯(PS)颗粒在二氧六环/水混合溶剂中的溶胀情况进行目视观察,可以看到,当减小混合溶剂二氧六环/水中的水含量时,PS颗粒从玻璃态到溶胀的玻璃态、溶胀的高弹态、流体态的转变,与PS颗粒升温时从玻璃态到高弹态、流体态的转变相对应.选定混合溶剂二氧六环/水(水6·8wt%)对一个单分散PS试样(Mw=1·68×105)在30℃进行分相平衡和溶胀平衡的测定.分相平衡是先将PS/二氧六环/水(混合溶剂水含量6·8wt%)体系加热到130℃使PS溶解成一均相溶液,然后在冷却过程中分相,在30℃达分相平衡(30天)时,浓相高分子体积浓度p″=0·304,稀相几乎为纯溶剂.从Flory-Huggins相平衡理论得出此体系的高分子-溶剂相互作用参数χ=0·63.本工作使用的单分散PS试样在选定的混合溶剂,即二氧六环/水(水6·8wt%)中,30℃时不能溶解只能溶胀,单分散PS颗粒淬冷试样(密度ρp=1·0451g/mL)到达溶胀平衡(80天)时浓相高分子体积浓度p″=0·308.而此淬冷试样经在80℃热处理100h后的老化试样(ρp=1·0470g/mL)达溶胀平衡(70天)时p″=0·312.从溶胀过程中浓相体积变化曲线可知试样经在80℃热处理过程中凝聚网络趋向于更均一,更接近热处理温度下的平衡态,试样密度增大,网络产生了新的链间凝聚,物理交联密度增大(凝聚点间分子量减小).从溶胀平衡理论并取χ=0·63(分相平衡)可得到淬冷试样的物理交联点间分子量Mc=11·6×104,老化试样的物理交联点间分子量Mc=6·9×104.实验结果说明溶胀过程及溶胀平衡的测定可以反映玻璃态高聚物中的凝聚网络结构的细节,而且非常敏感.     

Cohesional Entanglement of Amorphous Polymer in Glass State as Probed by Equilibrium Swelling in a "Non-Solvent

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Construction of ternary phase diagrams in nonsolvent/solvent/PMMA systems

In this work, the ternary phase diagrams in three nonsolvent/solvent/PMMA systems (n-hexane/n-butyl acetate/PMMA, water/acetone/PMMA, and n-hexane/acetone/PMMA) were constructed by theoretical calculation and experimental measurement. Binodal curves were calculated by using the Flory–Huggins theory for three-component systems and measured by titrating the PMMA solution with nonsolvent until the onset of turbidity. By using concentration-dependent nonsolvent/solvent and solvent/PMMA interaction parameters and constant nonsolvent/PMMA interaction parameters, good agreement has been obtained between the calculation and the measurement. The values of nonsolvent/solvent interaction parameters were taken from the literature sources, and the values of solvent/PMMA and nonsolvent/PMMA interaction parameters were measured by vapor sorption and swelling equilibrium, respectively. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 607–615, 1998     

Predicting the phase behaviour of solvent-modified epoxy resins

 The Flory–Huggins equation has been used to model the equilibrium phase behaviour of a solvent-modified epoxy resin intended for the fabrication of porous components by chemically induced phase separation followed by evacuation of the solvent after curing. Points in composition–temperature space corresponding to a transition from homogeneous to heterogeneous postcuring microstructures have been identified for a variety of solvents using a thermal gradient oven. Assuming this transition to coincide with the cloud-point curve corresponding to the gel point of the resin, the data were used in conjunction with the predictions of the Flory–Huggins equation to estimate the interaction parameter and its temperature dependence for each solvent. Phase diagrams in composition–conversion space were then calculated for a range of curing temperatures. Received: 20 September 1999 Accepted: 21 December 1999     

Thermosensitive phase behavior and drug release of in situ gelable poly(N-isopropylacrylamide-co-acrylamide) microgels

In situ gelable poly(N-isopropylacrylamide-co-acrylamide) microgels were prepared by precipitation polymerization in the presence of various amounts of N,N′-methlenebisacrylamide as a crosslinker. The diameters of microgels were in the range of 200–300 nm with narrow distributions as determined by photo correlation spectroscopy. The equilibrium swelling ratio and thermosensitive properties of the microgels increased with decreasing crosslinker content. The volume phase transition of microgels dispersions at high concentrations were investigated by phase diagrams. The microgels dispersions experienced four phases when the temperature was increased: semitranslucent swollen gel, clear flowable suspension, cloud flowable suspension, and white shrunken gel. The related phase transition temperatures were influenced by crosslinker content and the concentration of the microgel dispersions. Herein, the gelation temperature was changed by more than 20 °C, shrinking temperatures were slightly changed by about 3 °C, and cloud point temperatures showed almost no change. The three phase transition temperatures of microgels dispersed in phosphate-buffered saline solutions were lower than that in water. As drug carriers, the release rates of bleomycin from bleomycin-loaded microgel dispersions exhibited diffusion control at human body temperature.