| The rich phase behavior in physically associating polymer solutions(PAPS),which consists of the reversible gelation and phase separation,the fundamental explanations about them have existed for more than three decades.After that,many theories and methods have been used to account this system.But so far,many fundamental problems,such as the thermodynamic nature of the transition from a sol state to a gel state,and vice versa sol/gel transition,has not yet been clarified.Further,the explanations about new phenomena appearing in experiments challenge the theoretical physicists.Self-consistent field theory (SCFT),which is the most precise methods of the mean-field framework,is applied widely in the field of the assembly of block copolymers.Using SCFT the self-assembly of flexible-chain system is studied,and the results of the rigid block copolymers accounted by SCFT are also demonstrated by the related experiments.In contrast to the other mean-field methods, the advantage of SCFT,which begins with the analytic onset,can obtain the relatively accurate numerical result.Therefore,the lattice SCFT is applied to physically associating polymers to study the thermodynamic property and structure behavior in the paper,and the expectant results are obtained.There are two chain architectures for associating polymer.One is the physically associating polymer which has many associating points distributing along the backbone,the other is the physically associating polymer which only has end-associative points at the two ends of the chain.The systems of the two chain models are systematically studied in this paper.Further.the trial application of lattice external field dynamic method is that the assembly of rod-rod block copolymers is studied by the lattice SCFT and lattice external field dynamic method.This paper consists of four sections:In the first section,we study the phase behavior of PAPS.where the polymer has many associating points distributing along the backbone.Chain length of N=101 is considered, where each sticker monomer is regularly placed ten monomer apart.In the simulation,two inhomogenous structures in the solutions are observed.One is a micro-fluctuation homogenous(MFH) structure,the other is a randomly-closely packed micelle(RCPM) structure.The structure of the micelle in RCPM is similar to that of the "flower micelle" in the telechelic associative polymer system.When(?)P≥0.08 and the homogenous associating polymer solution is cooled,the MFH structure firstly appears,and the system transits from the homogenous solutions(HS) to the MFH phase entirely.If the solutions are cooled further,the RCPM structure appears.When(?)P＜0.08 the system immediately transits from the homogenous solutions(HS) to the RCPM morphology entirely when the polymer solution is cooled to be sufficiently low.At the same time,if(?)P＜0.53, a macroscopic phase separation accompanying the occurrence of RCMP occurs,where the polymer rich phase consists of RCPM morphology,otherwise the system entirely transits from MFH morphology into RCPM morphology.Furthermore,a peak appears in the temperature-dependent specific-heat curve CV(χ)/(?)P at each transition point.For the HS-MFH transition the peaks are unsymmetrical,i.e., CV(χ)/(?)P has an abrupt increase and a slow decrease,whereas for the MFH-RCMD phase transition CV(χ)/(?)P shows an approximately symmetrical character.Finally,the system in MFH phase may be trapped in one of the two energy basins in a experimental time scale. However,the appearance of RCPM structure means that the system is trapped in one of the series of "deeper" energy basins,and it is difficult to jump off this deep basin into one of the MFH or one of the other RCPM structures through thermal fluctuations.In the second section,the effect of the changes of chain architecture on the boundary of the phase is studied.The parameters of the architecture of chain is N and l.When the chain length increases when l=10 and N＞11,the boundary of the MFH occurrence occurs at lowerχand (?)P.However,the boundary of the micellar occurrence occurs in largerχ,and changes weakly.The triple point,which corresponds to the intersection between the boundaries of the MFH and micellar structures,moves to lower polymer concentration(?)tp.The above results demonstrate that MFH structure is dependent on the chain length,the increase of the chain length is favorable to the stability of MFH structure.Note that it is not observed in the system for N=11 in this simulation.This confirms the dependence of the MFH structure on the chain length.When l decreases from 10 to 6 for fixed N=61,the behavior of MFH morphology is similar to the case of the increase of chain length.However,the boundary of the micellar occurrence also goes down to the lowerχwhen decreasing l.When the chain length increases, the values of(?)tp for the different l systems basically satisfy the same functional relationship. For the boundary of the micellar occurrence,we examine wether the equation ln(φcmc)= A+B/T,where A,B are parameters,fulfils.When the chain length is short the functional relationship fulfils.The increase of chain length make it not fulfil,which is dependent on the l.In the three section,the phase behavior of end-associating polymer of symmetrical end block in a solvent is studied.Firstly,the effect of the number of sticker monomers of end block Nst on the boundary of micellar phase on the phase diagram is systematically studied.The variations of the micellar boundary with(?)P are different for different Nst systems.In the case of Nst=1,the saturate phenomenon occurs in the high(?)P range,i.e..the increase of(?)P does not continue to decrease the values ofχon the boundary of micellar phase.In the systems of Nst=2 and Nst=3,however,this saturate phenomenon disappears.Furthermore,the increase of Nst from 1 to 2 makes micelle occur in the regime of lower(?)P,whereas when Nst increases from 2 to 3,similar effect becomes much weaker and the critical micellar concentration almost does not change.Secondly,the variations of the micellar shapes with Nst and(?)P are studied.In the systems for Nst=1 and Nst=2.only sphere-like micelle is observed.In addition to sphere-like micelle,bulk micelle and worm-cylindrical micelle are observed in the system of Nst=3.Finally.the changes of the micellar numbers in the systems on the boundaries of the micellar phase are accounted in the cases of different Nst.The variation of the micellar number with(?)P is dependent on the magnitude of(?)P In the low range of polymer concentration, the increase of the micellar number with(?)P is very slow.In the intermediate range of polymer concentration,the micellar number increases slowly with(?)P.In the above two ranges of polymer concentration,the change of Nst has weak effect on the variation of micellar numbers with(?)P.In the high range of polymer concentration,the different behaviors are observed in the systems of different Nst.For Nst=1,the micellar numbers increase less 10%for a increase of(?)P= 0.1,which behaves hke the constant.For Nst= 2,there is a valley in the curve of the variation of the micellar number with(?)P,on the onset of the high range of polymer concentration.It may be relative to the changes of the positions of the near-neighboring micelles.There is a linear variation of the micellar number with(?)P in the system of Nst=3.In the fourth section,the self-assemble behavior of rod-rod diblock copolymers is studied by means of self-consistent field lattice model(SFLM) and external field dynamic lattice method(EFDLM).Firstly,using SFLM in the face center lattice,the self-assemble behavior of the rod-rod diblock copolymers is studied,and the phase diagram is constructed.It is shown that the order-disorder transition point of rod-rod diblock copolymers is lower than that of coil-rod diblock copolymers,which is consistent with the other theoretical prediction.Four stable structures are obtained,i.e.,overlapping cylinders,cylinders,lamellae and zigzag lamellae. Furthermore,tow metastable states are observed,i.e.,micelles and zigzag cylinders.Secondly,the forming processes of the lamellar,cylindrical and zigzag cylindrical morphologies are investigated by means of EFDLM.The three forming processes are divided into three stages:The collection of the same component occurs in the initial stage when the system behaves the doubled connected domains;In the intermediate stage the rudiment of the respective structure forms;In the final stage the system forms the ordered structure.The formation of biconnected domains from the relatively small domains,where some component is rich,is the common character of the forming processes of the three structures.Seen from the evolutive times of the above structures,the evolutive time of cylinder structure is much longer than those of the other two structures.This may be due to the formations of the zigzag cylinders in local sections of cylindrical rudiment in the evolving process(disappeared in the final stage).
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