Temperature effects in the mechanical desorption of an infinitely long lattice chain: Re-entrant phase diagrams

We consider the mechanical desorption of an infinitely long lattice polymer chain tethered at one end to an adsorbing surface. The external force is applied to the free end of the chain and is normal to the surface. There is a critical value of the desorption force ftr at which the chain desorbs in a first-order phase transition. We present the phase diagram for mechanical desorption with exact analytical solutions for the detachment curve: the dependence of ftr on the adsorption energy (at fixed temperature T) and on T (at fixed ). For most lattice models ftr(T) displays a maximum. This implies that at some given force the chain is adsorbed in a certain temperature window and desorbed outside it: the stretched state is re-entered at low temperature. We also discuss the energy and heat capacity as a function of T; these quantities display a jump at the transition(s). We analyze short-range and long-range excluded-volume effects on the detachment curve ftr(T). For short-range effects (local stiffness), the maximum value of ftr decreases with stiffness, and the force interval where re-entrance occurs become narrower for stiffer chains. For long-range excluded-volume effects we propose a scaling ftr~T1-(Tc-T)/ around the critical temperature Tc, where =0.588 is the Flory exponent and 0.5 the crossover exponent, and we estimated the amplitude. We compare our results for a model where immediate step reversals are forbidden with recent self-avoiding walk simulations. We conclude that re-entrance is the general situation for lattice models. Only for a zigzag lattice model (where both forward and back steps are forbidden) is the coexistence curve ftr(T) monotonic, so that there is no re-entranc

Analytical theory of finite-size effects in mechanical desorption

We discuss a unique system that allows exact analytical investigation of first- and second-order transitions with finite-size effects: mechanical desorption of an ideal lattice polymer chain grafted with one end to a solid substrate with a pulling force applied to the other end. We exploit the analogy with a continuum model and use accurate mapping between the parameters in continuum and lattice descriptions, which leads to a fully analytical partition function as a function of chain length, temperature (or adsorption strength), and pulling force. The adsorption-desorption phase diagram, which gives the critical force as a function of temperature, is nonmonotonic and gives rise to re-entrance. We analyze the chain length dependence of several chain properties (bound fraction, chain extension, and heat capacity) for different cross sections of the phase diagram. Close to the transition a single parameter (the product of the chain length N and the deviation from the transition point) describes all thermodynamic properties. We discuss finite-size effects at the second-order transition (adsorption without force) and at the first-order transition (mechanical desorption). The first-order transition has some unusual features: The heat capacity in the transition region increases anomalously with temperature as a power law, metastable states are completely absent, and instead of a bimodal distribution there is a flat region that becomes more pronounced with increasing chain length. The reason for this anomaly is the absence of an excess surface energy for the boundary between adsorbed and stretched coexisting phases (this boundary is one segment only): The two states strongly fluctuate in the transition point. The relation between mechanical desorption and mechanical unzipping of DNA is discusse

Polymer adsorption and its effect on colloidal stability : a theoretical and experimental study on the polyvinyl alcohol-silver iodide system

The purpose of this study was to gain insight in the factors determining the stability of hydrophobic sols in the presence of polymers, with the emphasis on the destabilisation of sols by polymers and the role played by salts therein.In chapter 1. the practical importance of polymer stabilisation and destabilisation is shown by several examples, a.o. in industrial applications, in water purification and soil structure improvement. Thereafter the choice of the PVA-AgI system as a model for this study was explained. PVA has a simple structure and is uncharged and its concentration in solution may be readily determined. This is important for adsorption measurements. AgI provides a good model for the dispersed phase: the properties of the electrical double layer on AgI in the presence of salts and low molecular weight organic substances have been investigated extensively and the specific surface area can be determined easily. Moreover, with a combination of PVA and AgI one has the advantage of being able to acquire information on the properties of the first layer on the surface by a comparison with known data on the butanol-AgI and ethylene glycol-AgI systems.The characterisation of the materials used is described in chapter 2. The specific surface area of AgI was determined by three independent methods. The results of these methods agreed well with each other. The average radius of the AgI particles turned out to be about 500 Å. From viscosimetric measurements on PVA solutions the molecular weights and configurational parameters of PVA, such as the radii of gyration, the length of a statistical chain element and the linear expansion factors were determined. In addition, it was shown that the PVA used is essentially uncharged.In chapter 3. the measurement of the amount of PVA adsorbed per ml is treated. The adsorption isotherm shows a pronounced high affinity character. The maximum amount adsorbed is 1-1.5 mg/m 2, depending on the molecular weight and the degree of hydrolysis of the PVA. The maximum adsorption increases somewhat with increasing molecular weight; for PVA with 12% of acetate groups it is distinctly higher than for PVA which is nearly completely hydrolysed. At maximum adsorption one fourth of the segments at most can be in contact with the surface; the remaining parts of the molecule protrude into the solution in the form of loops and tails. From measurements of the adsorption as a function of time and from 'two- step' adsorption experiments it could be deduced that the adsorption of segments is reversible. However, desorption of whole polymer molecules is not measurable.In chapter 4. measurements are described to obtain the layer thickness and the coverage in the first layer on the surface by PVA. From protection measurements qualitative information was obtained about the layer thickness. The protective power appeared to be slightly dependent on the molecular weight and to depend somewhat more strongly on the degree of hydrolysis of the PVA. The thickness of the adsorbed layer was viscosimetrically determined as a function of the amount adsorbed. The maximum layer thickness is about 100 Å. By measuring the electrophoretic mobility of polymer covered particles the layer thickness was likewise estimated. These results are in good agreement with the viscosimetric results.The coverage in the first layer on the surface was estimated from the shift of the point of zero charge and from the change in the surface charge on adsorption of polymer, in comparison with the same properties of AgI in the presence of butanol and ethylene glycol. A reasonable estimation for the percentage of the surface which is occupied by PVA turned out to be 70% for amounts adsorbed of more than half the maximum.With the help of these data the distribution of segments in the adsorbed layer could be obtained. For amounts adsorbed between 0.5 and 1.0 mg/m 2a HOEVE distribution applies. In the first layer on the surface the polymer volume fraction is about 70%. At a distance equal to the thickness of the first layer a discontinuity occurs, the volume fraction dropping to 56 %, and in the remaining part of the adsorbed layer the segment distribution is exponential. If more than 1 mg/m 2is adsorbed possible end effects occur: due to the presence of long tails at the ends of a polymer molecule the thickness increases more strongly with the amount adsorbed than predicted from the HOEVE distribution.The model for the segment distribution is somewhat oversimplified: it appeared to be impossible to account for the differences between different molecular weights at a given amount adsorbed.Results with respect to the flocculation of AgI by PVA have been given in chapter 5. Flocculation was found to be optimal if a special method is used for the mixing of PVA and Agl. Most efficient flocculation is obtained if a given volume of sol with uncovered particles is added to an equal volume of a sol with nearly completely covered particles. This phenomenon could be easily explained on the bridging model: flocculation occurs because loops of the adsorbed layer of one particle attach to the other. In this way a network of AgI particles interconnected by polymer bridges is formed. For the explanation of the efficiency of the way of mixing irreversibility of the adsorption of the polymer molecules is essential.Another important condition for efficient flocculation is the presence of a small amount of electrolyte. On these grounds the flocculation should be referred to as sensitisation. The minimum salt concentrations which are needed for flocculation are in the ratio of about 100:10:1 for salts with univalent, bivalent and trivalent counterions, respectively. Critical flocculation concentrations measured after a fixed time of flocculation were found to depend on the sol concentration. From measurements of the initial rate of flocculation, and from experiments in which the flocculation time was adjusted to the sol concentration, it was shown that this dependence on the salt concentration has a kinetic origin. The flocculation by bridging was found to be a bimolecular process.The critical flocculation concentrations were found to depend only slightly on the molecular weight of the PVA. For a PVA with a higher acetate content the amount of electrolyte needed was found to be significantly lower.In chapter 6. an attempt has been made to interpret the flocculation theoretically. To that order the free energy of interaction between a covered and an uncovered particle has been calculated. On account of the complicated nature of the problem only an approach for flat surfaces has been considered.In addition to the VAN DER WAALS attraction and the double layer repulsion the contribution to the free energy of interaction due to the adsorbed polymer has to be calculated. This contribution was formally split up in two terms, the first being the adsorption attraction due to the gain in free energy on account of the adsorption of segments on the second particle. The second term is the configurational repulsion which is caused by the entropy loss if a loop becomes two bridges by the adsorption of the middle segments of the loop. The fundamental assumption used to evaluate these two terms is that the number of segments which, at a given interparticle separation H , adsorbs on the second particle equals the number of segments which, in the absence of the second particle, would lie beyond a distance H from the surface. Using the theories of HOEVE and HESSELINK and the distribution of segments derived in chapter 4. these two polymer contributions to the free energy of interaction could be obtained.It was found that the VAN DER WAALS attraction is negligibly small in comparison to the other terms. The total free energy of interaction has the following characteristics. At small salt concentrations a maximum occurs at large distances due to the double layer repulsion, whilst at distances of some tens of Ångströms a minimum is present, sufficiently deep for irreversible flocculation. The function of salt is to suppress the maximum at large distances by partial compression of the double layer, so that the particles can approach each other to a distance corresponding to the minimum in the free energy. The system will then flocculate.Although the magnitude of the polymer contribution, especially at small distances, is somewhat doubtful on account of various approximations made, the theory does give a good explanation for the amount of salt, with ions of different valencies, which is needed for flocculation. The theoretical predictions with respect to the effect of the amount of adsorbed polymer agree also with the experimental observations. From this it follows that the theory is essentially correct. Indications were obtained that a theory which is applicable to spherical particles would agree even better with the experiments. The development of such a theory would be a promising next step.In conclusion, this study firmly establishes the bridging model for flocculation by polymer. It appeared possible to interpret several aspects quantitatively. Especially the function of indifferent electrolytes emerged clearly

Phase diagram for a mixture of colloids and polymers with equal size

We present the phase diagram of a colloid-polymer mixture in which the radius a of the colloidal spheres is approximately the same as the radius R of a polymer coil (q=R/a1). A three-phase coexistence region is experimentally observed, previously only reported for colloid-polymer mixtures with smaller polymer chains (q0.6). A recently developed generalized free-volume theory (GFVT) for mixtures of hard spheres and non-adsorbing excluded-volume polymer chains gives a quantitative description of the phase diagram. Monte Carlo simulations also agree well with experimen

Polymers at interfaces and in colloidal dispersions

This review is an extended version of the Overbeek lecture 2009, given at the occasion of the 23rd Conference of ECIS (European Colloid and Interface Society) in Antalya, where I received the fifth Overbeek Gold Medal awarded by ECIS. I first summarize the basics of numerical SF-SCF: the Scheutjens-Fleer version of Self-Consistent-Field theory for inhomogeneous systems, including polymer adsorption and depletion. The conformational statistics are taken from the (non-SCF) DiMarzio-Rubin lattice model for homopolymer adsorption, which enumerates the conformational details exactly by a discrete propagator for the endpoint distribution but does not account for polymer-solvent interaction and for the volume-filling constraint. SF-SCF corrects for this by adjusting the field such that it becomes self-consistent. The model can be generalized to more complex systems: polydispersity, brushes, random and block copolymers, polyelectrolytes, branching, surfactants, micelles, membranes, vesicles, wetting, etc. On a mean-field level the results are exact; the disadvantage is that only numerical data are obtained. Extensions to excluded-volume polymers are in progress. Analytical approximations for simple systems are based upon solving the Edwards diffusion equation. This equation is the continuum variant of the lattice propagator, but ignores the finite segment size (analogous to the Poisson-Boltzmann equation without a Stern layer). By using the discrete propagator for segments next to the surface as the boundary condition in the continuum model, the finite segment size can be introduced into the continuum description, like the ion size in the Stern-Poisson-Boltzmann model. In most cases a ground-state approximation is needed to find analytical solutions. In this way realistic analytical approximations for simple cases can be found, including depletion effects that occur in mixtures of colloids plus non-adsorbing polymers. In the final part of this review I discuss a generalization of the free-volume theory (FVT) for the phase behavior of colloids and non-adsorbing polymer. In FVT the polymer is considered to be ideal: the osmotic pressure Pi follows the Van 't Hoff law, the depletion thickness delta equals the radius of gyration. This restricts the validity of FVT to the so-called colloid limit (polymer much smaller than the colloids). We have been able to find simple analytical approximations for Pi and delta which account for non-ideality and include established results for the semidilute limit. So we could generalize FVT to GFVT, and can now also describe the so-called protein limit (polymer larger than the 'protein-like' colloids), where the binodal polymer concentrations scale in a simple way with the polymer/colloid size ratio. For an intermediate case (polymer size approximately colloid size) we could give a quantitative description of careful experimental dat