Mts2ZS_semiflextheta2002.pdf

401 Macromol. Theory Simul. 2002, 11, 401–409 Full Paper: Investigation of semiflexible coil-like chains in the process of partitioning with a slit in a solvent of variable thermodynamic quality has shown two key results. For semiflexible chains in a good solvent, the effect of chain stiffness played a role only at low concentrations. However, the situation is different with interacting chains where the effect of stiffness is also observed at higher concentrations. For theta chains, the partitioning into a slit in dilute solutions is lower for semiflexible than for flexible chains, while for higher concentrations this order is reversed. The packing ability of semiflexible chains at higher concentrations is enhanced in the theta system. Interestingly, stretching of chains on penetration into the slit is observed at higher concentrations. Decomposition of free energy change on partitioning into entropy and energy contributions gives more information on the details of partitioning of these systems, especially the differentiation between dilute and moderate concentration regimes. A positive change of partitioning entropy in the theta solvent in the semidilute regime for both flexible and semiflexible chains is noteworthy. This is related to breaking favorable interactions between chains on penetration into the slit. Partitioning coefficient K as a function of concentration bE for theta solutions of flexible (open symbols, dotted line) and semiflexible, A = 7, (filled symbols, solid lines) chains for slit widths D = 8, 12 and 20. Partitioning of Semiflexible Macromolecules into a Slit in Theta Solvent Zuzana Škrinµrovµ, Peter Cifra* Polymer Institute, Slovak Academy of Sciences, Dfflbravskµ cesta 9, 842 36 Bratislava, Slovak Republic E-mail: [email protected] Keywords: partitioning; Monte Carlo simulation; semiflexible macromolecules; stiffness; theta solvent; Introduction Partitioning of macromolecules between the small pores and the bulk solution forms the basis for various separation and characterization processes, and applications such as oil recovery or intercalation of nanocomposites. It is also of interest from a fundamental viewpoint. Partitioning into micropores has been studied mainly for flexible chains in a good solvent. There have only been a few studies that include chain stiffness[1] or variable solvent quality.[2–4] In this paper, we investigate both of these features together. In our previous work, we reported on the partitioning of semiflexible chains in a good solvent.[5] Introducing chain stiffness is part of a continuing effort to include realistic features of macromolecules such as excluded volume, thermodynamic quality of solvent, etc., in the behavior of macromolecular systems. Macromol. Theory Simul. 2002, 11, No. 4 While representing more realistic features of macromolecules, stiffer chains also pose a challenge to both the theory and the simulations, especially when interactions between chains and the effect of lower temperatures are included. An example of this new complexity is the recent studies of coil collapse and crystallization of semirigid chains.[6 – 10] Although the collapse transition has been well established over the last two decades for flexible chains, new work studying the case of more rigid chains has recently received much attention. It was found that while the theta transition changed only slightly with chain stiffness, the globule–solid transition shifted considerably.[6, 7] At low temperatures, a stable globular toroidal structure was established for higher stiffness.[8 – 10] Chain dynamics was also influenced by chain stiffness[11] and this plays a role in processes such as chain folding and crystallization. i WILEY-VCH Verlag GmbH, 69469 Weinheim 2002 1022-1344/2002/0404–0401$17.50+.50/0 402 Z. Škrinµrovµ, P. Cifra The objective here is to establish the partitioning behavior of semiflexible chains which are in the theta condition into a slit. In part, this is related to recent developments in the liquid chromatography of macromolecules, where it has been shown that better separation was achieved when the theta solvent condition was approached.[2, 12] In this respect, the whole range of solvent quality between the good and theta solvent is interesting, but here we will concentrate mostly on the limiting case of theta solvent and will remain in the coil-like regime, i. e., not using the highest rigidities (the rod-like macromolecules). In what follows, we first present our model of partitioning with the slit including chain rigidity, which is variable with the solvent quality and/or temperature. In the results section, we first present properties of single chains of variable rigidity over a range of solvent quality between good and theta solvents. Then we discuss partitioning at dilute concentration and study the penetration transition on increasing concentration as a function of confinement, solvent quality, and chain rigidity. A separate section is devoted to the decomposition of the free energy change on partitioning into thermodynamic contributions. Model and Monte Carlo Simulations In order to understand the effect of chain stiffness while investigating a large-scale phenomenon, equilibrium between a multichain solution and solution in the slit, we use a simple lattice chain model. Previously we investigated semiflexible chains in a good solvent and their partitioning with narrow slits.[5] This amounts to using selfavoiding walks on a cubic lattice with an extra energetic penalty, eg, for a kink (“gauche” bond) in the chain, which determines the stiffness of the chain and is defined as a nonlinear two-bond sequence in the chain. Within this approximation if the chain flexibility, eg = eg /kT F 0 (or if the temperature equivalently), is varied, the quality of solvent remains in the good solvent regime. When introducing variable thermodynamic quality of solvent one has to introduce molecular interactions, other than the basic volume exclusion based on the site occupancy. This is done effectively using an attractive interaction energy, es, between non-bonded nearest neighbour chain segments (either inter- or intra-chain) on the lattice. This effective interaction includes the effects of polymer–polymer, polymer–solvent and solvent–solvent interactions. It should be noted that the temperature of the system is also related to molecular interactions in the case of stiff chains and thus is related to the ratio, es = es / kT F 0. After defining the two variables, es and eg, we have two choices for their use: (1) es = es /kT = variable, eg = constant; (2) es = variable, eg = constant. The first case represents chains with a constant persistent length independent of temperature while the second case represents chains which become stiffer with decreasing tem- Table 1. Characteristics of the chains used in the simulation. f: flexible; sf: semiflexible. Solvent flexibility es eg Rg lps good good theta theta theta f sf f sf, A = 7 sf, A = 10 0 0 0.2693[25] 0.2387[7] 0.2208[7] 0 2.5 0 1.671 2.208 6.44 10.85 5.34 7.50 9.04 1.416 4.194 1.244 2.227 3.1126 perature. The first model was used for modelling of the collapse of semiflexible chains.[8, 9] For our study of semiflexible chains in a solvent of variable thermodynamic quality, this model is not suitable because it provides a positive temperature coefficient of coil dimensions in contrast to the common behavior of semiflexible chains in solution. In this study, we make use of the second case with the additional condition of a correlation between temperature/interactions and chain flexibility, eg = A es, where A is a constant characterizing chain stiffness and es is an independent variable here. This correlation leads to a decrease in flexibility with temperature, and in concentrated systems also to an orientation correlation between chains which is in accordance with previous studies.[6, 7, 13] The total energy of the system is given as: U = –nii es + ng eg (1) where nii is number of segment–segment contacts and ng is the number of “gauche” bonds. This parameterization allows for a rich behavior at low temperatures, in which there is a tendency towards a maximal number of contacts for more rigid chains. This, together with local barriers between microstates, creates frustration in the system. We will consider here, however, a coil-like regime at and above the h-temperature. Thus, the use of biased sampling techniques is not required,[6, 7] although close attention has to be paid to the phase diagram kT/es vs. A.[6, 7] While the h-temperature increases only slightly with the chain rigidity, A, the theta state for larger rigidities comes very close to the crystallization temperature. It was shown[7] that the globular phase between the good solvent solution and the crystal disappears at rigidities around A l 13. These states require the configurational bias sampling in simulation.[6, 7] Here, we used A = 7 and 10, for multichain systems only A = 7 was used (Table 1). The choice of these two values was led by the intention to use higher rigidities in a region of the phase diagram with a significant difference between theta and crystallization temperatures. Simulation of partitioning of macromolecules between a slit and bulk solution in a twin box system was described previously.[4, 14] Confined and free systems of chains are in direct contact with a free exchange of chains. The simulations provide the equilibrium concentrations of chains in the bulk and in the slit without a Partitioning of Semiflexible Macromolecules into a Slit in Theta Solvent need to calculate the confinement free energy from the respective chemical potentials. The partitioning coefficient K was obtained from the equilibrium concentrations, bI and bE, in the interior (I) of the slit and the bulk solution in exterior (E) after equilibration of chains between the twin box compartments. Confinement free energy used further is given by the formula DF/kT = –ln K. The distance of the walls in the slit was in the range D = 8–50 of lattice spacing units. The confinement was characterized by the ratio, k = 2Rg0 /D, where Rg0 is the radius of gyration of unconfined coils. We used the Metropolis Monte Carlo method with reptation updates of chains, as many as 7 6 109, with the number of chains ranging up to 616. Most of the results are obtained for a chain length of N = 100 beads, only in Figure 4 b values of N = 20–200 were used. Figure 1. Fraction of “gauche” bonds xg0 and mean-square radius of gyration pR2g0 P as a function of interaction energy es for flexible (A = 0, triangles) and semiflexible (A = 7, squares), (A = 10, circles) chains. Points with highest interaction energy at each curve represent the respective h-state. Results and Discussion A. Single Rigid Chain Properties The parameters used in the simulation and the respective single-chain properties in terms of radius of gyration, Rg, and persistence length, lps, are collected in Table 1. The persistence length was calculated exactly from the average of all bond projections on the first bond of a chain: lps ¼ * Nÿ1 X i¼1 a1 ai + . a ð2Þ and is indistinguishable from the approximate evaluation for the used range of rigidities.[5] Figure 1 and 2 depict the temperature dependence of the fraction of “gauche” bonds xg0, mean-square radius of gyration, pR2g0 P and persistence length, lps, of flexible and semiflexible chains with A = 7 and 10. The data are presented in the range between the high temperature limit and the respective h-state, which has been shifted slightly due to the introduction of chain rigidity. Chain dimensions decrease with temperature and result from a delicate balance between interactions and chain rigidity. Doye et al.[6] reported for the same chain model that the temperature coefficient of coil dimensions changed sign above the h-temperature at a certain rigidity. For lower rigidities, A a 5, dimensions started to increase with temperature, which is the opposite trend to what happens at higher rigidities, including those used here. Insight into the structure of coils formed by these semiflexible chains can be obtained by estimation of the single chain structure factor defined as: SðqÞ ¼ N X N 1 X sinðqrij Þ=qrij 2 N i¼1 j¼1 ð3Þ Log-log plots of S(q) vs. wave number, q, are depicted in Figure 3 a and b. Figure 3 a shows the behavior of flex- Figure 2. Variation of persistence length lps with interaction energy es for flexible and semiflexible chains. ible chains in the good solvent and in the h-state. Inserted lines with respective slopes next to the curves represent the theoretical exponents, which predict that S(q) scales to lq–2 for ideal chains, and lq–1.69 for good solvent conditions. One can recognize a good match for theta and good solvent situations with the predicted exponents. Figure 3 b shows the structure of coils for semiflexible chains. Interestingly, these are composed of two different regions. In the limit of high q, or smaller dimensions, the slopes of more rigid chains become very close to the slope –1 of the curve for a rigid chain. At lower values of q, or larger dimensions, the macromolecules become coil-like approaching the slopes of flexible chains either in good or theta solvent. It is clear that observation of the 403 404 Z. Škrinµrovµ, P. Cifra the theta conditions for partitioning with the slit. For more rigid macromolecules, the theta state is the limiting condition for use of these solutions. As explained above, this is caused by the proximity of theta and crystallization temperatures. Of course, for poor solvents, which are above the theta temperature, we can reach higher rigidities. Though relatively small rigidities are used here it will be shown further that they considerably affect the partitioning with the slit. It should also be noted that a previous study[5] showed that for rigidity eg = 2.5, close to the one used here, the exponent in the scaling of –ln K0 vs. k was already close to 1, which is characteristic of rigid rods, while the exponent for flexible chains was 1.69. B. Partitioning in Dilute Solutions Figure 3. (a) Structure factor S(q) vs. wave number q, plotted for flexible chains in good and theta solvents. (b) Structure factor S(q) for semiflexible chains in good (eg = 2.5) and theta solvents (A = 7 and 10) and for the rigid rod, for comparison. Inserted lines with indicated slopes are theoretical scaling predictions discussed in the text. semirigid macromolecules reveals a bimodal pattern. On a larger scale a coil-like behavior, and on a smaller scale a rod-like behavior. This behavior was reported recently in the simulation of amorphous polymer melts[15] or in the experimental scattering of solutions.[16] Though the pattern in S(q) on large and small scales is different, it does not mean that the coils are inhomogeneous. We also investigated the distribution of the end-to-end distance and found no effect of bimodality in the shape of this distribution except for an almost negligible shoulder for theta chains at A = 10. It should be noted that we do not reach the high stiffness values common for many semiflexible chains characterized by lps A 10. This is because we concentrate on We determined the partitioning coefficient K0 from the simulation of the system which consisted of a twin box with an open exchange of macromolecules between the free solution and the solution in the slit. These results are presented in Figure 4. The usual reduced plot used for plotting this type of results K0 vs. k, not shown here, exhibits relatively small differences for variable chain stiffness in this range of chain rigidities. This emphasizes the usefulness of such universal plot for representation of partitioning data as it was observed previously for the case of variable solvent quality.[4] Larger chain stiffness, however, leads to significantly larger increase of K0 for a given k, as reported by Davidson et al.[17] To show the differences in the curves we make a semi-logarithmic plot, Figure 4 a. Results were collected for D = 8–50 and N = 100. The curves for semiflexible h-chains with two flexibilities A = 7 and 10 are between the curves for chains of good solvent with eg = 0 and 2.5. Data for flexible chains in theta solvent are situated in this reduced plot along the data for flexible chains in a good solvent.[4] As seen in the case of a good solvent,[5] the stiffness shifts K0 to higher values for a given k. To avoid the possible conclusion from the reduced plot stating that the more rigid chains enter the slit more easily than the flexible ones, we also estimated K0 for D = 12 and N = 20–200 for the same model chains as in the reduced plot. In Figure 4 b we plot K0 for these results as a function of the contour length of chains, Lc = (N – 1) a. The order of the curves is now reversed showing that the flexible chains of the same length enter the slit more readily. C. Partitioning in Semidilute Solutions It has already been reported[2] that there is a delayed weak-to-strong penetration transition of macromolecules to the slit with an increasing concentration in theta solutions. In a good solvent, the partitioning of chains into the slit starts to increase at low concentrations (depending on Partitioning of Semiflexible Macromolecules into a Slit in Theta Solvent Figure 5. Partitioning coefficient K as a function of concentration bE for theta solutions of flexible (open symbols, dotted line) and semiflexible, A = 7, (filled symbols, solid lines) chains for slit widths D = 8, 12 and 20. Figure 4. (a) Partitioning coefficient K0 in dilute solution plotted as a function of k for flexible and semiflexible chains in the good solvent and semiflexible chains in the theta solvent. (b) Partition coefficient K0 as a function of the contour length Lc /D for D = 12 and N = 20–200 for chains as in (a), defined in insert. the slit width), whereas chains in the theta solution penetrate to the slit only at higher concentrations due to less repulsive interactions between the macromolecules. Zero initial slope of the concentration dependence of K in the theta solution is related to the zero second virial coefficient. At higher concentrations, higher order interactions become important and repulsion between chains drives the macromolecules into the slit. The concentration dependence K vs. bE of flexible and semiflexible chains at theta conditions is shown in Figure 5 for comparison. For three slit widths D = 8, 12, and 20 (representing confinements k = 1.33, 0.89, 0.53 for A = 0, and k = 1.88, 1.25, 0.75 for A = 7), the concentration dependence of the partitioning coefficient for theta flexible and theta semiflexible chains is presented. All the concentration dependent curves start with a zero slope. A small change in es shifts the system away from the h-state, resulting in a positive or negative initial slope in the case of a higher or lower thermodynamic quality of solvent, respectively (not shown here). Partitioning coefficients for more rigid chains start at lower values in the dilute solution because of the larger size of more rigid coils. On increase of the concentration, the partitioning of these semiflexible chains into the slit starts to increase at a rate that is interestingly, higher than for flexible macromolecules. At a certain concentration, the respective curves for flexible and semiflexible coils cross and at higher concentrations, we observe a reversed order in partitioning characterized by easier partitioning of semiflexible chains into the slit. Furthermore, this difference at higher concentrations is influenced by the confinement k, one can observe for more narrow slits a stronger penetration in comparison to flexible chains. It should be noted that for athermal semiflexible systems the effect of stiffness played a role only at low concentration.[5, 18] With interacting chains close to the theta point, we observe the effect of stiffness also at high concentrations as described above. It seems that this has to do with the ability of chains to fill the depletion layer at the walls. In the case of a good solvent, it was already concluded by Yethiraj[19] that there was an increased packing ability of more rigid chains, which was well demonstrated especially close to the wall. In the case of favorable interactions between chains near the theta point, additional packing ability is probably contributing to a higher penetration to the slit. This stems from the orientation correlation between chains that forces chains to line up locally. Our results may lead to a modification 405 406 Z. Škrinµrovµ, P. Cifra This represents a larger sensitivity of K to the solvent change near the theta point for the more rigid chains. Common behavior of flexible and semiflexible chains at high temperatures (es approaching zero), Figure 6 b, is characteristic for the model used here. The rigidity introduced in the model does not survive higher temperatures. In order to introduce an entropic rigidity, except the energetic rigidity (coming from rotational isomerization), we would have to introduce a certain amount of fixed rigid structures into chain, which would not surrender to temperature increase. We can compare the above results to the experimental results on partitioning by Satterfield et al.[20] (polystyrene in porous glass) or by Tong and Anderson[21] (poly(ethylene glycol) in polyacrylamide gels), both in good solvent conditions. They also observed an increase of partitioning with the concentration of the solute and a decrease with the confinement. Likewise, Lal, Sinha and Auvray[22] showed for polystyrene in the Vycor porous glass that the penetration of chains in the porous medium is almost complete for a concentration of 20% over a broad range of molecular weights. A detailed comparison of our results for variable chain flexibility, however, is hampered by the experimental problem to vary the chain stiffness in a single set of experiments. Experiments at the near theta solvent condition, while having the potential for an improved separation in liquid chromatography[12] are still rare.[23] D. Contributions to Free Energy Change on Partitioning into the Slit Figure 6. (a) Comparison of penetration transition of flexible chains in good and theta solvent (dotted lines) with that of semiflexible chains (A = 7) (solid line) in the theta solvent at D = 8. (b) Sensitivity of the partitioning coefficient K to the change of solvent quality from a good to theta solvent for flexible and semiflexible chains as indicated by arrows in (a). of the conclusions of Dickman[18] that there is no effect of stiffness on pressure at higher concentrations for the case of favourably interacting chains. Since the weak-to-strong penetration transition is very different in athermal and theta chains, Figure 6a, an important question arises on how K is changing with this change of solvent quality for flexible and semiflexible chains. In Figure 6 b we compare these changes in partitioning in a narrow range of concentrations bE = 0.355– 0.399 chosen to be in the range of a large difference in the weak-to-strong penetration transition between the good and the theta solvent. Figure 6 b shows variations of K with es for flexible and semiflexible chains. In the range of good solvents for both flexible and semiflexible chains (A = 7) the partitioning changes only slightly. When approaching the theta solvent conditions, the partitioning into the slit decreases more rapidly for more rigid chains. Decomposition of the free energy change DF on partitioning of the coils into entropy and energy contributions gives new information about this process. In the case of good solvent, the whole penalty is of entropic nature. For the theta solvent, the zero concentration dependence of K (or DF), (Figure 7 a) at low concentrations is a result of opposite tendencies in entropy and energy changes. Surprisingly, in comparison to the good solvent situation, a positive DS appears on the transition of the coil into the slit in theta solvent over a broad range of concentrations in semidilute solution. This behavior can, however, be explained. Flexible Theta Chains DU: At small concentration bE, individual coils entering the slit are bent when confined and form more favorable contacts within the coil, DU a 0 (Figure 7a). With an increase of bE, on penetration into the slit the average number of favorable contacts for a single chain decreases. This is because more of the chains are in the presence of the noninteracting walls as chain numbers increase in the slit, and because of the breaking of clusters of chains pro- Partitioning of Semiflexible Macromolecules into a Slit in Theta Solvent theta solution. As we know from the dimensions of flexible coils in theta solution the effect of clusters increases approximately up to the coil overlap concentration b* = 0.207 (for N = 100). On further increase of bE, the conditions I/E are balanced and DS steadies. But even at the highest concentration both DU and DS do not decrease to zero (while DF does) because of the presence of walls in the slit, which restrains mutual contacts between chains relatively to the situation in bulk. Semiflexible Theta Chains Figure 7. (a) Decomposition of the free energy change in partitioning with the slit into energy and entropy contributions for flexible chains in theta solvent. (b) Decomposition of the free energy change in partitioning into energy and entropy contributions for semiflexible chains (A = 7) in the theta solvent. D = 12 for (a) and (b). duced by favorable contact on penetration into the narrow slit, thus DU A 0. Relatively low concentration in the slit also contributes probably to a smaller possibility of forming favorable contacts in the slit. On further increase of bE, conditions I/E become closer and DU settles. At high concentrations, a smaller proportion of the chains in the slit experience a change in the environment from the bulk and the energy penalty decreases further. –TDS: At small bE we obtain the classical picture, DS a 0, in which individual chains are constrained in possible conformations when entering the slit. As the concentration is increased, the entropy must reflect breaking of favorable contacts between chains when they penetrate into the slit. Already at bE = 0.1 the entropy change becomes favorable, DS A 0. Apparently, this has to do with interruption of the transient cluster network in the In the theta solution of semiflexible chains, the energy change DU on penetration into the slit consists of two contributions: chain flexibility, DUg, and contacts interaction, DUii, Figure 7 b. We can see similar behavior of components to the one of flexible chains, with the exception of high concentrations. DU and –TDS at high concentration not only compensate but both approach zero. Again, there is a remarkable positive change of entropy on confinement in the semidilute regime, a marked difference from the usual situation in the dilute regime for good solvent. DUii is negative in the dilute regime and positive in the whole range of semidilute concentrations as in the previous case. DUg is positive except at very high concentrations and reflects the bending of chains on entering the slit. Interesting is DUg a 0 for the highest concentrations, which points to a surprising stretching of chains on entering the slit. Figure 8 shows the meansquare end-to-end distance pR2P and the fraction of “gauche” bonds xg in regions E and I at equilibrium with increasing bE for D = 12. External dimensions do not change with the concentration. This is in contrast to flexible chains, which exhibit a slight maximum.[3] Thus, semiflexible theta chains are closer to ideal behavior than flexible theta chains. In our previous study on semiflexible chains in good solvent[5] the coil size decreased with concentration in both regions E and I. Respective dimensions in the slit are smaller but increase at highest concentrations. This is consistent with the direct experimental observation of chains in the Vycor porous glass by Lal, Sinha and Auvray[22] showing that the radius of gyration of the confined chains is always smaller than the radius of gyration of the free chains in an equivalent bulk solution. The large decrease of xg with concentration (especially in region I) while the coil dimensions do not increase considerably is interesting. This indicates “prefolding” with formation of parallel trans-sequences that enable the decrease in the number of “gauche” bonds while the overall size of coils does not change. The small value of DU at high concentration, in contrast to the situation in flexible chains, is the result of compensation between the two contributions to energy. The transition to negative DUg at high concentrations is related to the packing of chains and the theta state. As 407 408 Z. Škrinµrovµ, P. Cifra Figure 8. Concentration dependence of the mean-square endto-end distance pR2P and the fraction of “gauche” bonds xg in bulk solution and at respective concentration in the slit at equilibrium. was shown in theta solution,[2] because of favorable contacts between chains, the depletion layer is broader compared to the good solvent and filling of depletion layer appears only at higher concentrations. Here, at filling of the more and more narrow depletion layer at high concentrations the chains also stretch. The reluctance of theta chains to fill the depletion layer thus disappears at high concentration and the profile resembles that of the good solvent where the chains are able to approach the walls more closely. Recently there appeared tendencies to physically include the solvent molecules[24] instead of modelling the solvent conditions effectively as used here. Solvent molecules included in the model can probably bring more insight to the subtle effects described above. E. Concentration Profiles The concentration profile between the slit walls presents useful additional microscopic information about chains partitioning into the slit. A comparison of the profiles in good and theta solvents at similar concentrations showed[2] that there was an extensive depletion layer in the theta solution. This behavior was attributed to the formation of chain clusters in theta solution. A comparison of the profiles formed by flexible and semiflexible chains in the good solvent was presented elsewhere,[5] and showed similar profiles at dilute solutions and the enhanced ability to fill the depletion layer at the wall by more rigid chains at higher concentrations. This was attributed to the better packing ability of the more rigid chains. In Figure 9, we present concentration profiles for theta chains, which are either flexible (A = 0) or semiflexible (A = 7). Referring to the curves of K vs. bE, Figure 5, we present profiles below and above the penetration transition for D = 12. At lower concentrations, we observe a Figure 9. Concentration profiles bI(x) in the slit at two average concentrations for theta chains that are more rigid (A = 7) (bI = 0.0426 and 0.302, solid lines) or flexible (bI = 0.0484 and 0.287, dotted lines). higher concentration of flexible chains in the slit, while above the transition there are more rigid chains in the slit. From the shape of the profile it is clear that especially at higher concentrations there is an enhanced ability of more rigid chains to fill the depletion layer at the slit walls. It is natural to compare also all four profiles of flexible and semiflexible chains either in good or theta solvent at the same concentration in the slit. We compared all these profiles at two concentrations bI = 0.050 and 0.327 in a slit-only simulation. The order of the profiles at higher concentration in the order of increasing depletion at the walls is: good solvent semiflexible, flexible, theta solvent semiflexible and flexible chains. Both theta solutions have deeper and broader depletion layers. At lower concentration, this differentiation is not so clear and profiles of flexible chains in the good solvent and semiflexible chains in theta solvent are tumbling. Conclusions An investigation of semiflexible coil-like macromolecules in the process of partitioning with a slit in a solvent of variable thermodynamic quality has shown the complex behavior of these systems. While for athermal (with respect to interactions) semiflexible systems, the effect of chain stiffness plays a role only at low concentrations, the picture is different for interacting chains. The effect of stiffness is also apparent at higher concentrations. For theta chains, we can conclude that partitioning into a slit in dilute solutions is lower for semiflexible than for flexible chains, while for higher concentrations this order is reversed. The packing ability of semiflexible chains at higher concentrations is Partitioning of Semiflexible Macromolecules into a Slit in Theta Solvent enhanced in the theta system, as seen from the partitioning coefficient and from concentration profiles. At higher concentration, a surprising stretching of chains on penetration into the slit is observed. Decomposition of the free energy change on partitioning into entropy and energy contributions shed more light on details of partitioning of these systems, especially on the differentiation between regimes of dilute and moderate concentration. A positive change of entropy on penetration into the slit in the theta solvent in the semidilute regime for both flexible and semiflexible chains, which is related to breaking of favorable interactions between chains, is noteworthy. Partitioning of semiflexible macromolecules for separations in liquid chromatography is possible in poor solvent but should be performed above the theta condition for the more rigid chains. Acknowledgement: Financial support from Slovak Academy of Sciences (SAS) under 2/7076/21 is acknowledged. Authors wish to thank I. Teraoka and T. Bleha for valuable discussion. Usage of computational resources of Computer Center of SAS is acknowledged. Received: November 26, 2001 Revised: February 21, 2002 [1] T. 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