copolymerizing different 
 monomers offers vast possibilities to 
 tune the properties of covalent copolymers .
in fact , the ability to 
 copolymerize monomers in an alternating , gradient , random , or block 
 manner offers superb precision in the control over the copolymer s 
 molecular structure ( composition , sequence , and length ) . as a result
generally , the molecular structure of the 
 copolymer can be predicted and tuned by a delicate interplay of reactivity 
 and feed ratios of the two monomers via the classical copolymer equation , in combination with advanced controlled polymerization 
 techniques . in the field of supramolecular 
 copolymers , in contrast
, much less attention 
 has been devoted to developing 
 predictive rules that allow to forecast the sequence , composition , 
 and length of multicomponent mixtures .
the dynamic nature of the non - covalent 
 interactions makes multifunctional supramolecular copolymers versatile 
 systems , which gives them a high potential for use as adaptive materials , in organic electronics , and as biomimetic systems .
however , 
 constructing hierarchical multicomponent co - assemblies is particularly 
 challenging as it requires a rational design that encompasses a subtle 
 balance between the complementary recognizing motifs for connecting 
 different monomers into an ordered array and the compatibility between 
 the diverse peripheral functional groups .
moreover , important differences 
 are encountered when copolymers made under thermodynamic equilibrium 
 are compared with those prepared under kinetic control .
when mixing 
 different types of monomers , two extreme assembly cases may occur ; 
 total self - sorting or complete co - assembly of the different monomers . 

many elegant examples have been presented in which multicomponent 
 co - assembly has been achieved by aromatic donor  acceptor interactions , hydrogen bonding , -stacking interactions , and 
 others .
in addition , multicomponent systems 
 are also found to form self - sorted assemblies . a comprehensive molecular understanding
recently , significant 
 progress has been made in the elucidation 
 of pathway complexity , mechanistic detail , feed - dependent behavior , 
 thermodynamic stability , composition , and stack length of supramolecular 
 ( co)polymerizations .
exciting examples are found in kinetically controlled 
 living copolymerizations as developed for covalent block copolymers and small molecules , which show that kinetically trapped block structures can be formed 
 in supramolecular copolymers . for systems under thermodynamic equilibrium , 
 a combined experimental and theoretical approach proved to be a robust 
 method to unravel several issues , although these endeavors were typically 
 limited to one - component or simple two - component systems .
however , in many examples reported on multicomponent systems , these 
 characteristics remain largely elusive , particularly when the components 
 aggregate via different supramolecular polymerization mechanisms . in the past
, our group has extensively studied the helical , one - dimensional 
 self - assembly of chiral and achiral alkyl - substituted btas ( alkyl - btas ) , which follows a 
 highly cooperative mechanism in dilute aliphatic solvents .
the handedness of the helical superstructures , p or m , is biased by the presence of a 
 non - racemic stereocenter in the aliphatic side chains .
in contrast , 
 the self - assembly of btas functionalized with short oligodimethylsiloxane 
 ( odmsi ) chains ( odmsi - bta ) revealed a decrease in propensity 
 for assembly compared to alkyl - substituted btas , which was attributed 
 to the presence of sterically crowded siloxanes .
the presence of odmsi side chains in bta - derivatives increased 
 the critical aggregation concentration 10100 times over that 
 of alkyl - btas , but the mechanism of self - assembly remained 
 unclear .
in addition , we also observed that unsymmetrical btas comprising 
 both odmsi and alkyl side chains form a superlattice in the bulk due 
 to strong phase separation of the two chemically incompatible side 
 chains .
an intriguing question 
 is how btas with either odmsi or alkyl side 
 chains would interact in solution . in a mixture of alkyl - bta and odmsi - bta ,
three outcomes are possible : ( 1 ) alternate 
 copolymerization to minimize steric demand of odmsi - btas ; ( 2 ) complete self - sorting due to peripheral chain incompatibility ; 
 or ( 3 ) everything in between . to elucidate these possibilities , we 
 herein perform  sergeant - and - soldiers  experiments between opposite pairs of chiral and achiral alkyl - bta and odmsi - bta derivatives ( scheme 1 ) . a combination 
 of chiral ( optically active ) and achiral btas permits the observation 
 of copolymerization behavior by circular dichroism ( cd ) spectroscopy . 

an unexpected chiral induction was observed from the mixture of two 
 independently cd - silent solutions of achiral alkyl - bta ( a - bta ) and chiral odmsi - bta ( r - si - bta ) .
a detailed analysis 
 was conducted to understand how the differences in molecular structure 
 and polymerization pathway of individual monomers affect the chiral 
 amplification and the overall copolymerization process by combining 
 spectroscopic studies with in - depth theoretical modeling . in the present 
 work ,
we propose a general experimental / modeling approach to understand 
 various aspects of supramolecular copolymerization under thermodynamic 
 control .
this collective approach permits us to successfully elucidate 
 the monomer feed - dependent copolymerization behavior and thereby the 
 composition of the supramolecular copolymers obtained . in the present 
 report , before studying the copolymerization between alkyl - bta and odmsi - bta , we first revisit the mechanism of homopolymerization 
 of the individual components .
the copolymerization is then analyzed 
 by the mixing of the two monomers in different ratios .
finally , we 
 put forward a new theoretical model that permits to fully explain 
 the copolymerization process .
before studying the copolymerization behavior , 
 we first analyzed the mechanism of homopolymerization of the individual 
 monomers .
the self - assembly of chiral r - si - bta in methylcyclohexane ( mch ) was probed using 
 temperature- and concentration - dependent cd measurements and compared 
 to that of achiral a - bta under identical conditions . 

the experimental cooling curves were fitted with a one - component 
 mass - balance model ( figures s1 and s2 ) .
this model is based on the equilibrium between monomers , oligomers , 
 and polymers , and the aggregation process is divided into a nucleation 
 regime and an elongation regime . the equilibrium constant kn describes the formation of a nucleus , whereas ke describes the equilibrium constant in the 
 elongation phase .
the nucleation step is highly unfavorable in a cooperative 
 process so that kn < ke . in an isodesmic process , kn and ke are equal .
the degree of cooperativity 
 in the supramolecular polymerization is given by the cooperativity 
 factor  defined as kn / ke .
the thermodynamic parameters 
 obtained for a - bta and r - si - bta are summarized in table 1 and detailed in the supporting information .
the he of 35 kj / mol for r - si - bta in combination with  = 1 indicates 
 that the assembly is enthalpically driven and occurs via an isodesmic 
 mechanism .
interestingly , at lower concentration ( 10 m in mch ) , 
 the uv  vis spectrum ( figure s3 ) 
 shows aggregation but the solution of r - si - bta is cd silent ( figure 1b ) .
this suggests the formation of ( disordered ) 
 dimers or short aggregates ( referred to as x - type 
 aggregates ) which comprise a different conformation of the hydrogen 
 bonds that hardly contributes to the cd signal .
as inferred from the 
 one - component model and expected for an isodesmic mechanism , the x - type aggregates predominantly consist of dimers at this 
 low concentration ( figure s4 ) .
in contrast , 
 under identical conditions ( 10 m in mch ) a - bta cooperatively self - assembles into equal amounts of right - handed 
 ( p ) and left - handed ( m ) helical 
 aggregates of significantly longer length ( average stack length of 
 over 200 monomers per stack at 298 k ) , with thermodynamic parameters 
 consistent with those previously found for similar btas .
these aggregates are known to be stabilized 
 by ordered , three - fold helical hydrogen bonding .
( a ) cd spectra of s - a - bta ( blue trace ) , si - bta ( yellow trace ) , and the mixture 
 ( green trace ) of s - a - bta ( 4 mol% ) + si - bta ( 96 mol% ) at ctot = 10 m in mch at 298 k. ( b ) cd spectra of r - si - bta ( blue trace ) , a - bta ( yellow trace ) , and the mixture ( green trace ) of r - si - bta ( 4 mol% ) + a - bta ( 96 mol% ) 
 at ctot = 10 m in mch at 298 k , 
 showing chiral amplification from two individually cd - silent solutions . 

( c ) experimental and calculated ( vide infra )  ( determined 
 from the cd effect at 220 nm ) as a function of the percentage of sergeant r - si - bta added to the soldier a - bta at ctot = 50 m at 
 three different temperatures .
experimental data are represented by 
 a dashed line and calculated values by a solid line .
( d ) cd spectra 
 of various mixtures of a - bta and r - si - bta at ctot = 50 m at 293 k. more insight into the differences of the hydrogen bonding 
 patterns 
 between the two btas was inferred from infrared ( ir ) spectroscopy 
 measurements .
the comparison of the ir spectra of 1.0 mm mch solutions 
 of a - bta and r - si - bta shows different c = o vibration bands of the homopolymers suggesting 
 differences in the hydrogen bonding patterns within the aggregates 
 formed by a - bta and r - si - bta ( figure s5 ) .
the introduction 
 of the three sterically demanding odmsi groups at the periphery of 
 the bta core not only destabilizes the self - assembly as elucidated 
 from its lower enthalpy of elongation he ( 35 kjmol ) 
 compared to a - bta ( 65 kjmol ) but also alters the nature of the hydrogen bonds within the aggregates . in our previous work
experiments on scalemic mixtures of s - si - bta / si - bta and s - a - bta / a - bta . in both 
 cases ,
a complete helical sense bias was achieved at 10 mol% for s - si - bta and only 4 mol% for s - a - bta .
we continued with investigating 
 the supramolecular copolymerization between alkyl - bta and odmsi - bta of opposite pairs of chiral s - a - bta and achiral si - bta , and of chiral r - si - bta and achiral a - bta , respectively ( scheme 1 , figure 1a , b ) . all the four monomers feature an identical three - fold 
 self - complementary amide array that can recognize either monomers 
 of identical or different side chains for homopolymerization or copolymerization , 
 respectively .
the molar circular dichroism values (  ) 
 of the individual solutions and the mixtures were measured at a total 
 bta concentration of 10 m in mch . strikingly , we here 
 find that a mixture of 4 mol% of chiral s - a - bta mixed with the 96 mol% of achiral soldiers si - bta is cd silent ( figure 1a ) , although s - a - bta on its own shows a large cd signal (  = 38 
 lmolcm ) .
this 
 could be due to three possibilities : ( 1 ) the chiral sergeant s - a - bta fails to bias the helicity 
 of the achiral si - bta soldiers due to immiscibility between s - a - bta and si - bta , resulting from side chains incompatibility ; ( 2 ) the fraction of s - a - bta is too small ( 4 mol% ) to bias the helicity of 
 the si - bta stacks ; or ( 3 ) si - bta fails to 
 form long aggregates at the applied concentration ( 9.6 m ) . 

this third possibility is supported by the theoretical one - component 
 model which shows that , at the applied concentration of 10 m , si - bta predominantly exists as dimers in mch ( figure s4 ) .
contrastingly , in the opposite 
 set of experiments where r - si - bta plays the role of sergeant , 
 4 mol% of the chiral sergeant r - si - bta did successfully bias the helical preference of a 
 large excess ( 96 mol% ) of achiral a - bta soldiers .
figure 1b shows appearance 
 of a large cd signal within the mixture , indicative of strong chiral 
 amplification , while the two homopolymer solutions were cd - silent . 

such observation is not unique but still 
 remarkable in the sense that the strong cd effect arises from the 
 mixing of two cd - silent dilute solutions , underlining a strong interaction 
 between the two monomers .
combining the two sets of experiments , we 
 conclude that odmsi - bta is a  good sergeant  
 for the alkyl - bta soldiers ( figure 1b ) whereas a  bad soldier  
 for alkyl - bta sergeants ( figure 1a ) .
therefore , unlike previously reported 
 sergeants , we present herein a bta that effectively biases the helical 
 sense preference of achiral alkyl - based btas , but is incapable to 
 efficiently function as a soldier .
this observation is in line with 
 those for crowded amino - acid - based btas recently disclosed by us and 
 bouteiller and co - workers , which were also excellent sergeants for 
 achiral alkyl btas .
to investigate 
 the copolymerization in more detail , we gradually 
 increased the fraction of the r - si - bta sergeant in a mixture with a - bta soldiers , 
 keeping the total monomer concentration constant at 50 m , and 
 monitored the changes in the molar circular dichroism (  ) 
 at 220 nm at three different temperatures .
a nonlinear variation of 
  was observed , and two distinct regimes were distinguished 
 ( figure 1c ) . in the 
 first regime , a strong nonlinear increase in the molar circular dichroism 
 was observed with the addition of r - si - bta sergeant . at 293 k , a maximum was reached at 4 mol% , 
 which coincides with the fraction of sergeant reported earlier for 
  sergeant - and - soldiers  experiments with aliphatic alkyl - btas . however , above 10 mol% of r - si - bta , a continuous decrease of the molar 
 circular dichroism was observed , reaching a minimum at 100 mol% r - si - bta .
this observation indicates 
 that at higher fraction of bulky r - si - bta another process is taking over that either decreases 
 the helical sense bias or affects the nature of the formed supramolecular 
 aggregates .
this observation is also in sharp contrast to  sergeant - and - soldiers  

experiments earlier performed between either chiral and achiral alkyl - btas or odmsi - btas , that revealed near 
 saturation in the cd - signal above 10 mol% of the alkyl sergeant . in order to elucidate the origin of this intriguing behavior 
 of r - si - bta in the mixed 
 aggregates , 
 we closely inspected the full cd spectra of all the mixtures with 
 increasing fraction of r - si - bta .
two distinctly different patterns in the shape of the cd spectra 
 can be discerned ( figure 1d ) : at low fractions of sergeant , up to 10 mol% , the 
 cd spectrum shows a double cotton effect with a maximum at 220 nm 
 and a shoulder at 245 nm , but at higher fractions of sergeant 
 ( > 25 mol% ) , the cd spectrum changes to the spectrum of pure sergeant , 
 with a single maximum at 225 nm .
such differences in the cd spectra 
 of the mixtures can be attributed to a different packing of the hydrogen 
 bonds within the helical stacks below 10 mol% and above 25 mol% r - si - bta .
the difference in molecular packing was also evident from the ft - ir 
 data of 1 mm mch solutions of 10 mol% and 90 mol% of r - si - bta that showed resemblance with pure a - bta and r - si - bta , respectively ( figure s5 ) . to further elucidate this change in the 
 shape of the cd signal 
 as a function of increasing fraction of r - si - bta ,
variable - temperature uv and cd experiments 
 were carried out at various compositions of r - si - bta / a - bta in mch at a total 
 bta concentration of 50 m ( figures 2 and 3 ) .
interestingly , 
 two different trends in the uv and cd cooling curves are observed . 

up to 5 mol% of r - si - bta sergeant added , all the uv cooling curves are superimposable to 
 the curve of pure a - bta , indicating a similar cooperative 
 mechanism of copolymerization as observed for a - bta homopolymer 
 ( figure 2a ) .
however , 
 above the threshold of 5 mol% of r - si - bta , the melting curves gradually become more sigmoidal 
 ( figures 2b and 3b ) , indicating a change toward an isodesmic growth 
 mechanism .
temperature - dependent uv spectra of solutions containing different 
 ratios of r - si - bta / a - bta probed at  = 220 nm with ctot = 50 m in mch ( cooling rate = 2 kmin ) .
( a ) going from violet curve ( 0 mol% r - si - bta ) to red curve ( 5 mol% r - si - bta ) , upon addition of 1 mol% , 2 mol% , 
 3 mol% , and 4 mol% of r - si - bta to a - bta .
( b ) going from violet curve ( 10 mol% r - si - bta ) to red curve ( 100 mol% r - si - bta ) , upon addition of 25 
 mol% , 50 mol% , and 75 mol% of r - si - bta to a - bta .
experimental and computed ( vide infra ) cd cooling curves probed 
 at  = 220 nm with ctot = 50 m 
 in mch containing different ratios of r - si - bta / a - bta ( cooling rate = 2 kmin ) . ( a ) going from violet curve ( 0 mol% r - si - bta ) to red curve ( 5 mol% r - si - bta ) , upon addition of 0.5 
 mol% , 1 mol% , 2 mol% , 3 mol% , and 4 mol% of r - si - bta to a - bta .
( b ) going from 
 violet curve ( 10 mol% r - si - bta ) to red curve ( 100 mol% r - si - bta ) , upon addition of 25 mol% , 50 mol% , and 75 mol% of r - si - bta to a - bta .
experimental 
 data are represented by dashed lines , while computed values are represented 
 by solid lines . to rationalize these 
 observations
, we hypothesize that the two 
 monomers can copolymerize into aggregates in which the monomer present 
 in majority dictates the molecular packing / aggregate properties . at 
 lower fractions of r - si - bta , a - bta dominated cooperative helical
aggregates are 
 formed contributing to the huge cd signal whereas at higher fractions 
 of r - si - bta , r - si - bta dominated isodesmic aggregates 
 ( x - type ) are assembled but participate with low cd 
 intensity . as the current experimental techniques available do not 
 allow defining the precise nature of the assemblies at such low concentration , 
 we resort to theoretical models to understand the copolymerization 
 in more detail .
a model describing two - component copolymerization was put forward 
 to explain the origin of the remarkable chiral amplification followed 
 by steep fall in the cd signal observed in the  sergeant - and - soldiers  

experiments performed between independently cd - silent solutions of a - bta ( named a in the model ) and r - si - bta ( named si in the model ) .
this new model is an 
 extension of the one - component model , but now with two monomers and 
 three types of aggregates , namely p , m , and x. the current model takes into account not 
 only distinct dimers and elongation steps but also the types of bonds 
 formed between different monomers in the stacks .
the reaction scheme 
 is described as a sequence of stepwise monomer associations and dissociations , 
 where the equilibrium constants are assumed to depend not only on 
 the aggregate type but also on the types of the two monomers involved 
 in the bond formed / broken , and whether it concerns the nucleation 
 of a new aggregate or the elongation of an existing one ( see supporting information section b for details ) . 

the equilibrium concentrations of all species are obtained by solving 
 the mass - balance equations for the two monomers , and these are subsequently 
 used to calculate theoretical cd and/or uv absorption cooling curves . 

this methodology has been applied previously to describe both the 
  majority - rules  and the  sergeant - and - soldiers  
 principles in cooperative two - component bta supramolecular polymerization .
herein , we assume that r - si - bta forms enantiomeric isodesmic x - type aggregates ( with thermodynamic parameters as reported 
 in table 1 ) while the a - bta forms racemic cooperative aggregates with two opposite 
 helicities , i.e. , p- and m - type 
 aggregates , with equal likelihood ( again with thermodynamic parameters 
 as reported in table 1 , ga - pm ) .
moreover , 
 we assume that a - bta can mix into x - type 
 aggregates ( ga - x ) and , vice versa , that r - si - bta can mix into both p- ( gsi  p ) and m - type ( gsi - m ) aggregates , by forming a - bta / r - si - bta bonds . 
 additionally , we consider that the formation of r - si - bta / r - si - bta bonds within cooperative p- and m - type aggregates and a - bta / a - bta bonds in isodesmic x - type aggregates are energetically 
 unfavorable , therefore they are not considered in the model
. an optimal 
 fit of the theoretical cd curves ( figure 3 , solid lines ) with the experimental cd curves 
 ( figure 3 , dashed lines ) 
 is obtained with the thermodynamic parameters shown in table 2 ( see supporting information section b for details ) .
figure 4 shows that the uv melting curves calculated 
 by this newly developed two - component model also demonstrate nice 
 agreement with the experimental curves ( figure 2 ) .
note that these uv curves are results 
 of the model , with parameters that were fitted only with cd curves , 
 which further illustrates the potential of the model to describe the 
 experimental data . calculated uv curves obtained from the model showing the 
 theoretical 
 normalized absorbance as a function of temperature .
( a ) going from 
 violet curve ( 0.5 mol% r - si - bta ) to red curve ( 5 mol% ) , upon addition of 1 mol% , 2 mol% , 3 mol% , 
 and 4 mol% of r - si - bta to a - bta .
( b ) going from violet curve ( 10 mol% r - si - bta ) to red curve ( 100 mol% r - si - bta ) , upon addition of 25 
 mol% , 50 mol% , and 75 mol% of r - si - bta to a - bta .
these model results show a 
 similar spectral trend as observed in the experimental uv cooling 
 curves in figure 2 .
as is evident 
 from the thermodynamic parameters of the copolymerization 
 as a function of the temperature in figure 5 , the mixing of r - si - bta into m- or p - type aggregates is less favorable than the addition of a - bta ( ga - pm < 
 gsi  p and ga - pm < gsi - m ) .
however , because of 
 the chirality of r - si - bta , this sergeant intercalates slightly better into p - type aggregates than into m - type aggregates ( gsi - m > gsi  p ) .
in addition , the incorporation 
 of a - bta and r - si - bta into x - type aggregates is less energetically favorable 
 than their incorporation into cooperative p- or m - aggregates ( ga - pm < ga - x and gsi 
temperature - dependent free energies ( g=h  ts ) of the co - assemblies 
 compared with those of the homopolymers .
apart from quantifying the thermodynamic parameters , this 
 model 
 also reveals the distribution of different species present at each r - si - bta fraction as a function 
 of temperature via speciation plots ( figure 6 ) . at lower fractions 
 of the sergeants r - si - bta , the cooperative mechanism of a - bta assembly ( p- and m - type ) dominates over the isodesmic 
 assembly of the x - type aggregates , and a competition 
 between p- and m - type stacks
is 
 observed ( figure 6a  c ) . 
 without sergeants , p- and m - type 
 aggregates are equally abundant ( figure s6 ) , while with increasing fractions of sergeants ( > 0.5 mol% )
, the p - type aggregates rapidly prevail over the m - type aggregates . the lower the temperature , the smaller the fraction 
 of sergeant needed to solely have p - type aggregates . 

the largest quantity of p - type aggregates is obtained 
 with a fraction of r - si - bta of around 10 mol% , which is in agreement with the experimental observations . 
 moreover , for higher fractions of sergeants ( > 25 mol% ) , the isodesmic x - type aggregates start to compete with the p - type aggregates ( figure 6d , e ) . when the quantity of r - si - bta is preponderant ( > 75 mol% ) ,
the isodesmic x - type aggregates prevail over the cooperative p - type aggregates ( figure 6f ) , and a dominant isodesmic mechanism is observed in the 
 mixture resulting in a fall in the cd intensity .
figure 7a shows the calculated amounts 
 of different species formed as a function of the addition of sergeants 
 at 293 k and predicts the coexistence of p- and m - type aggregates above 10 mol% of sergeant added . for p - type aggregates ,
the number of monomers per aggregate 
 decreases when the fraction of sergeants increases ( figure 7b )
. calculated concentration 
 of btas in the various species types ( p , m , and x ) and concentration 
 of free monomers ( a and si ) as a function of the temperature for several 
 fractions of sergeants r - si - bta : 0.5 mol% ( a ) , 4 mol% ( b ) , 10 mol% ( c ) , 25 mol% ( d ) , 50 mol% ( e ) , 
 and 75 mol% ( f ) .
( a ) calculated concentration 
 and ( b ) average stack length ( number 
 of monomers per stack ) of the various species types over the fraction 
 of sergeants r - si - bta at 
 293 k , ctot = 50 m in mch . to gain insight into the composition 
 of the distinct aggregate 
 types ,
the percentages ( figure s7 ) and 
 concentrations ( figure s8 ) of sergeants r - si - bta constituting the p- and x - type aggregates over sergeants 
 added were plotted , clearly indicating that the compositions of the 
 two aggregate types are not constant . with increasing fraction of 
 sergeants in the mixture , up to approximately 85 mol% , where the fraction 
 of p - type aggregates becomes negligible , the fraction 
 of r - si - bta in the p - type aggregates increases sub - stoichiometrically , up to 
 a limit of approximately 30 mol% .
this analysis suggests that above 
 the fraction of 10 mol% of r - si - bta ( where the cd signal is maximum ) , its propensity to intercalate 
 into p - type aggregates becomes lower , which initiates 
 the formation of segregated r - si - bta - dominated x - type aggregates in the mixture . as per the model prediction
, we conclude that the drop in the cd 
 intensity with increasing fraction of the sergeants is the outcome 
 of a reduction in both the amount and the average stack length ( number 
 of monomers per stack ) of cooperative p - type aggregates . 

since in the  sergeant - and - soldiers  experiment the 
 total monomer concentration remains constant , the amount of a - bta dominated p - type aggregates continuously 
 decreases with increasing r - si - bta / a - bta feed ratio thereby causing depletion in the cd 
 signal . by working instead in a solution with increasing fraction 
 of r - si - bta for a fixed 
 concentration of the achiral a - bta ,
the model with the 
 same thermodynamic parameters predicts a steady rise in the cd signal 
 rather than the drop observed in the  sergeant - and - soldiers  
 experiment ( figure 8a ) , due to continuous formation of x - type aggregates 
 in the presence of an invariant amount of p - type 
 aggregates . ( a ) experimental and calculated cd signal at 220 nm and ( b ) calculated 
 concentrations of the various species types over increasing fraction 
 of sergeants r - si - bta at 
 a fixed concentration of a - bta 25 m at 293 k. to experimentally validate this 
 prediction , we performed a new 
 set of experiments .
cd spectra were measured from a set of solutions 
 prepared at fixed ca - bta = 25 m and increasing concentration of r - si - bta ( figure 8a , figure s9 ) . 

indeed an overall rise in the cd signal is observed , with two different 
 slopes in the two regimes that can be rationalized by the model .
the 
 first regime , up to 2.5 m of r - si - bta ( i.e. , 9 mol% of r - si - bta ) , exhibits a chiral amplification corresponding 
 to the intercalation of r - si - bta into p - type aggregates . in the second part of the 
 titration curve ( cr - si - bta > 2.5 m )
, the 
 continuous 
 addition of chiral r - si - bta displays a small enhancement in the cd signal due to limited further 
 intercalation of r - si - bta in p - type aggregates as well as the formation of x - type aggregates ( figure 8b ) .
since the contribution of the helical columnar p - type aggregates to the cd signal is significantly larger 
 than the contribution of the short x - type aggregates , 
 only a small rise is observed in the cd intensity in the second regime 
 compared to the sharp jump in the first regime .
the continuous increase 
 in the cd intensity in this experiment rules out the possibility of 
 copolymerization of all the monomers into a single stack type ( x - type ) .
the formation of only x - type aggregates 
 would result in a significant drop in the overall cd signal due to 
 the dominance of r - si - bta , analogous to the drop observed in the  sergeant - and - soldiers  

experiment described in figure 1c . in fact , the presence of two regimes perfectly matches 
 with the coexistence of p - type and x - type aggregates , as predicted by the model .
based on the experimental data and the mathematical 
 model , the 
 entire copolymerization process as studied by the  sergeant - and - soldiers  

up to nearly 10 mol% of r - si - bta , favorable incorporation 
 of r - si - bta into p - type aggregates takes place in a cooperative mechanism , 
 such that the concentration of p - type aggregates 
 rapidly increases at the expense of m - type aggregates , 
 leading to chiral amplification . below 10 mol% of r - si - bta in the mixture ,
the steric hindrance 
 of bulky r - si - bta does 
 not adversely affect its behavior as a sergeant for a - bta , rather r - si - bta prefers 
 to randomly intercalate within predominantly a - bta - based 
 aggregates to minimize its own steric repulsion .
however , at 25 mol% 
 of r - si - bta added , the 
 shape of the cd spectra starts to change indicating a change in the 
 packing within the aggregate .
most likely , the incompatibility between 
 the alkyl and the odmsi side chains in combination with the isodesmic 
 assembly of the increasing amounts of r - si - bta overrules the favorable steric parameter for 
 copolymerization .
this plausibly results in the formation of segregated r - si - bta dominated short x - type aggregates , in the presence of p - type aggregates in the mixture . with increasing r - si - bta / a - bta feed ratios
, the 
 amount of a - bta dominated p - type aggregates 
 continuously drops in the mixture leading to a consistent fall in 
 the cd signal observed in the second regime .
additionally , due to 
 the coexistence of a significant population of the free r - si - bta monomer in the mixtures ( figure 7a ) , the compositions 
 of the p- and x - type aggregates 
 change continuously with added r - si - bta . illustrated are various species 
 types present below 10 mol% and above 25 mol% of r - si - bta added . for clarity , the presence of 
 free a - bta monomers in the system is omitted , as its 
 concentration is very low . in conclusion , 
 we reported supramolecular copolymerization under 
 thermodynamic equilibrium conditions between two bta monomers that 
 bear structurally different alkyl and odmsi side chains and are distinguished 
 by distinct self - assembly mechanisms .
their co - assembly behavior was 
 analyzed by  sergeant - and - soldiers  cd experiments and 
 in - depth theoretical modeling .
a remarkable chiral induction was observed 
 by mixing of two individually cd silent diluted solutions resulting 
 from supramolecular copolymerization between two monomers stacking 
 via cooperative and isodesmic mechanisms .
the two regimes observed 
 in the variation of the cd signal of the mixtures were related to 
 the combined effect of sterically demanding self - assembly of r - si - bta , the odmsi side chain s 
 incompatibility with a - bta , and the difference in mechanism 
 of the homopolymerization of the individual monomers .
below 10 mol% 
 of r - si - bta , the huge chiral 
 amplification originates from the favorable cooperative copolymerization 
 of a - bta soldiers with chiral r - si - bta sergeant into p - type aggregates , 
 in which the r - si - bta sergeants 
 completely copolymerize with a - bta to minimize their 
 own steric hindrance . beyond 25 mol% , the effect gradually diminishes 
 due to both side - chain incompatibility and isodesmic assembly of the 
 dominant bulky r - si - bta monomer , resulting in the segregated formation of r - si - bta dominated x - type aggregates along with p - type aggregates . as 
 the amount of a - bta monomers and thereby p - type aggregates continuously decreases with increasing r - si - bta / a - bta feed ratios , 
 we observe a continuous drop in the cd signal that predominantly arises 
 from the helical columnar p - type aggregate , explaining 
 the biphasic behavior . an excellent agreement between the experimental 
 results and the 
 model allowed us to quantify the thermodynamic parameters , the concentrations , 
 and the compositions of different aggregates present in the mixtures 
 as a function of various monomer compositions and temperatures during 
 the copolymerization .
this example is an illustration of how subtle 
 balances between several parameters such as different monomer compatibilities , 
 relative monomer reactivities , and individual mechanism of homopolymerization 
 are more critical in the construction of supramolecular copolymers 
 than established for covalent copolymerization .
the present work is 
 another step toward developing the understanding on the largely unknown 
 area of multicomponent supramolecular copolymerizations in the context 
 of the mechanistic elucidation , thermodynamic stability , and monomer 
 feed - dependent copolymerization behavior .
we propose that such a generalized 
 understanding combining spectroscopic studies with explicit theoretical 
 modeling on the complexity of supramolecular copolymerization will 
 pave the way for constructing more complex functional supramolecular 
 materials for future applications .
 supramolecular copolymers , 
 non - covalent analogues of synthetic 
 copolymers , constitute a new and promising class of polymers . 
 in contrast 
 to their covalent counterparts , the details of their mechanism of 
 formation , as well as the factors determining their composition and 
 length , are still poorly understood . here , 
 the supramolecular copolymerization 
 between two slightly structurally different benzene-1,3,5-tricarboxamide 
 ( bta ) monomers functionalized with either oligodimethylsiloxane ( odmsi ) 
 or alkyl side chains is unraveled by combining experimental and theoretical 
 approaches . by applying the  sergeant - and - soldiers  
 
 approach using circular dichroism ( cd ) experiments , we are able to 
 obtain detailed insights into the structure and composition of these 
 supramolecular copolymers . moreover , we observe an unexpected chiral 
 induction upon mixing two independently cd - silent solutions of the 
 achiral ( soldier ) and chiral ( sergeant ) monomers . 
 we find that the 
 subtle differences in the chemical structure of the two monomers impact 
 their homopolymerization mechanism : whereas alkyl - btas cooperatively 
 self - assemble , odmsi - btas self - assemble in an isodesmic manner . 
 the 
 effect of these mechanistic differences in the supramolecular copolymerization 
 process is investigated as a function of the composition of the two 
 monomers and explicitly rationalized by mathematical modeling . 
 the 
 results show that , at low fractions of odmsi - bta sergeants ( < 10 
 mol% ) , the polymerization process is cooperative and the supramolecular 
 helicity is biased toward the helical preference of the sergeant . 
 
 however , at higher fractions of odmsi - bta sergeant ( > 25 mol% ) , 
 the 
 isodesmic assembly of the increasing amounts of sergeant becomes more 
 dominant , and different species start to coexist in the copolymerization 
 process . 
 the analysis of the experimental data with a newly developed 
 theoretical model allows us to quantify the thermodynamic parameters , 
 the distribution of different species , and the compositions and stack 
 lengths of the formed supramolecular copolymers existing at various 
 feed ratios of the two monomers . 
Introduction
Results
Discussion and
Conclusions