Critical adsorption of an end-grafted diblock copolymer on a flat surface

Abstract

The critical adsorption of a single flexible diblock copolymer A_nB_m on a flat surface selective to block A is investigated by using the Monte Carlo simulation method. The surface is modeled as attractive to block A but inert to block B, whereas the head monomer A is grafted on the surface. The results show that the critical adsorption temperature, T_c, and the crossover exponent, φ, are the same as that of homogeneous polymer A_n for large n values. Although the B block decreases the A block surface-contact number and lowers the adsorption temperature of the finitely long polymer, the effect is eliminated with the increase in the length of the A block. However, we find that the B block has no influence on the mean asphericity parameter of the A block at T_c.

Introduction

Polymers tethered to surfaces have an important role in various biological processes.^{1, 2, 3, 4} The adsorption of the polymer can modify the surface and interfacial properties, and the degree is dependent on the number of adsorbed monomers. The polymer tethered to the surface can improve or prevent the adsorption of proteins on the surface. For example, the design of biocompatible materials requires reducing the adsorption of proteins on the surface of the material, leading to low platelet adhesion that reduces thrombus formation.² Therefore, understanding the physics of adsorption and desorption of the polymer with one end tethered to a surface is useful to design special surfaces with improved biocompatibility.¹ Surfaces coated with polymers are also relevant to many applications in industrial and biological technologies such as chromatography,^5,6 polymer compatibilization,^7,8 medical implants and bioaffinity sensors.⁹ The behavior of polymers near attractive surfaces has been extensively studied in theory and by computer simulation.^{10, 11, 12, 13}

A single homogeneous polymer interacting with a flat surface has been well investigated to identify the phase transition from a desorbed state to an adsorbed state with a temperature decrease beyond a critical adsorption point (CAP) T_c.^{11, 12, 13, 14, 15, 16, 17, 18, 19} Crossover scaling laws for a variety of quantities below, above and at the CAP have been formulated and verified by Monte Carlo (MC) simulation of self-avoiding walks.¹¹ Every monomer contacting the surface is assigned a monomer-surface attraction energy −E (or scaled energy ɛ=E/k_BT with k_B being the Boltzmann constant and T the temperature). The CAP can be interpreted as a second-order phase transition at the temperature T=T_c in the thermodynamic limit when the chain length N proceeds to infinity. The number of surface contacts, M, scales as M∼N^φ at the CAP. Much attention has been paid to the location of the CAP, the scaling behavior at the CAP and the determination of the crossover exponent, φ. The crossover exponent, φ, is somewhat disputable and lies in a range between φ=0.59^11,14,15 and φ=0.5.^{14,20, 21, 22} Recently, the scaling relationship for the adsorption of a single chain has been tested by MC simulation on a cubic lattice,^{15, 16, 17, 18, 19} and the adsorption transition of a polymer is well known.^{17, 18, 19, 20, 21,22}

Although extensive investigations of the CAP of homogeneous polymers have been carried out, there are few studies on the adsorption transition of copolymers. The self-consistent field theory was generalized to describe the adsorption of block copolymers.²³ The density profile of the adsorbing block A for the diblock copolymer A_nB_m is similar to that of the homogeneous polymer A_n. Then, the less adsorbing or non-adsorbing block B exists as a dangling tail.²³ The scaling properties of copolymers in the vicinity of the CAP have been investigated.^{24, 25, 26, 27} For random copolymers, the critical adsorption temperature increases with an increase in the fraction of adsorptive monomers of the chain while the crossover exponent φ=0.59 remains constant.²⁵ In recent study, the adsorption of a regular multiblock AB copolymer on a solid planar surface was mapped on an effective homogeneous polymer adsorption problem.^24,26 The CAP and the fraction of adsorbed monomers were found to be dependent on both the chain length and the block size of the attractive block A.²⁴

In the present study, the behavior of an end-grafted diblock copolymer A_nB_m with the head monomer A tethered to a flat surface is simulated using the MC method. We consider a specific case where the surface is attractive to monomer A but inert to monomer B, which is a limitation of a general case where the surface attraction of monomer A is stronger than that of monomer B. We have calculated the mean number of monomer A in contact with the surface. The critical behavior of block A is studied using finite-size scaling analysis on the mean contact number. We found that the critical adsorption temperature of A_nB_m is the same as that of the homogeneous polymer A_n if n is large. Our results indicate that the tail block B does not change the CAP of A_nB_m if the surface attraction of monomer A is stronger.

Materials and methods

The diblock copolymer A_nB_m is embedded in a simple cubic lattice. The chain comprises n type-A monomers and m type-B monomers consecutively linked with fluctuating bonds. The bond length between successive monomers along a chain can be taken from the set {(1, 0, 0), (1, 1, 0), (1, 1, 1)} by symmetry operations of the simple cubic lattice.²⁸ We adopt a self-avoiding walk chain with each monomer occupying one site of the lattice. The flat surface located at z=0 is assumed to be infinitely large and impenetrable to the copolymer chain. Here, the direction z is perpendicular to the flat surface. The copolymer chain is restricted to lie in the upper half space (z>0), and the first monomer A is fixed at position (0, 0, 1) that contacts the center of the flat surface (0, 0, 0). We use a large simulation system along the xy directions parallel to the surface and along the z direction perpendicular to the surface. Periodic boundary conditions are applied in the x and y directions. In addition, the box size along the x, y and z directions is larger than the polymer length n+m.

A monomer located at the layer z=1 is named the surface-contacted monomer. However, monomers A and B contacting the surface have different interaction energies E_A and E_B, respectively. In this work, we consider a copolymer with a stronger surface attraction of monomer A. Therefore, we assign an attractive energy E_A=−E for surface-contacted monomers A, whereas E_B=0 for monomers B. This parameter set is a limitation for copolymer with stronger surface attraction of monomer A, that is, |E_A|>|E_B|. The interaction between two non-bonded monomers of the same or the opposite type is purely repulsive and it is assigned as E_AA=E_BB=E_AB=0 in the simulation.

At the beginning of the MC simulation, a self-avoiding walk diblock copolymer chain A_nB_m is grown using the Rosenbluth–Rosenbluth growing method²⁹ with the first monomer A fixed at the surface. After creating the whole copolymer chain, we let it undergo a series of Brownian motion. In the dynamic model, a monomer is chosen randomly and a move is attempted for the monomer moving one lattice unit choosen randomly from one of the six directions ±x, ±y, ±z. This trial move will be accepted if the following five conditions are simultaneously satisfied: (1) the new site is located above the surface (z>0), (2) the new site is not occupied by any other monomers, (3) the new bond vectors belong to the allowed bond set, (4) no bonds cross and (5) the Boltzmann factor exp(−ΔE/k_BT)>p, where p is a random number uniformly distributed in (0,1) and ΔE is the change in energy after the trial move. In the simulation, we set the interaction strength E and the Boltzmann constant k_B as unity, that is, E=1. Therefore, the unit for temperature is E/k_B. In one MC step (MCS), all of the monomers in the polymer chain attempt to move once.

We adopt an annealing method to simulate polymer properties at different temperatures. Starting from a high temperature T=8, we slowly decrease the system temperature, T. The temperature step ΔT is chosen as small as 0.05 near T_c, whereas a slightly greater value of ΔT is chosen further from T_c. The final configuration at the previous temperature is used as the initial configuration for the subsequent temperature. At each T, the copolymer is first equilibrated for ~τ=2.5N^2.13 MCS.¹⁴ Then, we record polymer conformations at every 0.1τ MCS in the next 100τ MCS. Therefore, we collect 1000 conformations in each run. In our simulation, 2000 independent runs are used, and then the final results are averaged over 2 × 10⁶ independent configuration samples.

Results and Discussion

Critical adsorption

The CAP of polymers can be determined by analyzing the number of surface-contact monomers M at different temperatures. To this end, the surface-contact numbers of the diblock copolymer A_nB_m are calculated. The surface-contact number of monomer B is close to 0 because of the non-attractive property of B, whereas that of monomer A is relatively large and dependent on the temperature. Therefore, the A block is strongly adsorbed on the surface at low temperatures, whereas the B block dangles above the surface. In this work, we investigated how the adsorption behavior of the A block is affected by the tail block B.

We at first consider a simple case with m=n. The relationship between the mean surface-contact number of monomer A, <M_A>, and the length of the block A, n, is studied. For the adsorption of the homogeneous polymer A_n, the surface-contact number M can be expressed as a finite-size scaling against the chain length n and the temperature, T.^17,30 We apply finite-size scaling analysis for the adsorption of the A block in the diblock copolymer A_nB_n. Thus, <M_A> can be expressed as

where φ is the crossover exponent and T_c is the critical adsorption temperature. <M_A> shows different behaviors at temperatures above and below the critical point T_c because the second term (T−T_c)(n+1)^1/δ in the scaling form (1) changes sign for temperature, T, of annealing from T>T_c to T<T_c. Therefore, <M_A> has the best power law behavior at T=T_c, which can be expressed as:

Figure 1 presents the dependence of <M_A> on n at different temperatures for the diblock copolymer A_nB_n. One can see that the upward concave curves at low temperatures (T=1.45, 1.60) change to downward convex curves at high temperatures (T=1.65, 1.80). Therefore, the critical adsorption temperature, T_c, of the A block is located among the region (1.60, 1.65) according to the finite-size scaling theory.^17,18,30 The location of T_c is estimated by analyzing <M_A> using the finite-size scaling theory. The values of <M_A> at other temperatures in the interval (1.60, 1.65) can be obtained by quadratic interpolation from the simulation data. The best power law fit is achieved at T=1.625 for the A block of the diblock copolymer A_nB_n, indicating that T_c=1.625 for the infinitely long copolymer A_nB_n. It is interesting that the T_c of the long A_nB_n is the same as that of a homogeneous polymer with the same model.¹⁷ At T_c=1.625, we obtain the exponent φ=0.51, which is also close to that of the homogeneous polymer φ=0.52.¹⁷ The results clearly show that the tail block B does not change the CAP and critical exponents of the infinitely long copolymer A_nB_n if the surface attraction of monomer A is stronger.

Figure 1

Log–log plot of the mean number of surface contacts <M_A> versus the block length n at temperatures T from 1.45 to 1.80. Here, n is varied from 5 to 200. The straight, dotted line at T_c=1.625 is a linear fit.

However, the tail block B can change the contact number as well as conformational properties of the finitely long copolymer A_nB_n. We find that the <M_A> of A_nB_n is smaller than that of A_n because of the tail block B. Figure 2 presents the contact number fraction of monomer A <M_A>/n as a function of the temperature, T, for the different block lengths n=25, 50, 100 and 200. The <M_A>/n clearly increases below T_c. We find that the <M_A>/n decreases with an increase in n at high temperatures, whereas it is roughly independent of n at low temperatures. These results indicate a second-order adsorption transition for the long copolymer A_nB_n, in agreement with that of the homogeneous polymer.^11,17 To investigate the effect of the block B, we calculated the value of f_<M> for the contact number of A_nB_n compared with that of A_n:

Figure 2

Plot of the mean surface-contact number of monomer A <M_A> at different temperatures, T, for the diblock copolymer A_nB_n with different block lengths n=25, 50, 100 and 200. The inset shows the ratio f_<M> of the <M_A> of the diblock copolymer A_nB_n to that of the homogeneous polymer A_n at different temperatures.

This value is a ratio of the contact number of monomer A in the diblock copolymer A_nB_n to that of the homogeneous polymer A_n. The relationships between the ratio f_<M> and the temperature, T, are shown in the inset of Figure 2. One can see that f_<M><1, indicating that the non-adsorbed B block weakens the adsorption of the A block. Interestingly, the ratio f_<M> exists at a minimum at T=T_c and is roughly independent of the block length n at T=T_c. Specifically, we have . This result can explain why T_c and φ are the same for the copolymer A_nB_n and for the homogeneous polymer A_n. However, the ratio f_<M> varies with the A block length n at other temperatures deviating from T_c. The ratio f_<M> increases with an increase in the length n, meaning that the adsorption properties of the A block are less affected by the B block for the long-chain copolymer.

Next, we investigate a general case for the diblock copolymer A_nB_m to study the influence of the B block on the adsorption of the A block. We compared the dependence of the surface-contact number of the A block, <M_A>, on the length of the A block, n, for three chains A_n, A_nB₁₀ and A_nB₂₀ at the critical adsorption temperature T_c=1.625. The double logarithmic relationship for <M_A>-n is shown in Figure 3. We find that <M_A> decreases with an increase in the length of the B block because the dangling B block prevents adsorption of A monomers near the B block. However, we find that the curves <M_A>-n of A_nB₁₀ and A_nB₂₀ become closer to that of A_n with an increase in the block length n, meaning that the influence of the B block is eliminated with the increase in n. We also find that these curves are roughly parallel at large n values, which is consistent with the same value of φ for A_n and A_nB_n.

Figure 3

The mean surface-contact number of block A, <M_A>, for polymer A_nB_m with m=0, 10 and 20 at T_c=1.625. The inset presents the reduction of contact number Δ<M_A> because of the B block.

In addition, the reduction of the contact number because of the B block is calculated. The results are presented in the inset of Figure 3 for A_nB₁₀ and A_nB₂₀. The Δ<M_A> increases with n for short chains; however, it tends to be saturated at large n values. This result clearly shows that the influence of the B block is finite and tends to be 0 at large n values. Therefore, one could find that the <M_A>-n curves are roughly parallel at large n values in Figure 3. In addition, one could expect that these curves would overlap at much larger n values. Therefore, we can conclude that the CAP and critical exponents of the diblock copolymer A_nB_m is the same as that of A_n at large n values.

At finite temperatures, the adsorption of monomer A is a dynamic process. The influence of the tail block B on the dynamic behavior of the A block is also investigated. The probability that each monomer A is in contact with the surface P_A is calculated for the homogeneous polymer A₁₀₀ and for the diblock copolymers A₁₀₀B_m with m=50 and 200 at T=1.6 near CAP. The P_A is calculated as an average contacting event averaged over times and samples. The values of P_A are shown in Figure 4 in a log–log plot against the fraction of monomer positioned in the A block. Here, x=i/n represents the fractional position of the ith monomer, where i is a sequence order from the head monomer A (i=0) to the end monomer A (i=n−1). P_A(i=0)=1 is not included in the plot. One can see that P_A decreases with x, which can be attributed to two factors: a monomer locates away from the surface as x increases and the rear block behind the monomer prevents its adsorption. The increase in P_A at tail positions for the homogeneous polymer is because of the decrease in length of the rear block. For the homopolymer A₁₀₀, we find a power-law dependence for P_A, that is, P_A∝x^−0.45 at T=1.6. The power-law behavior changes from a downward curve above T_c to an upward curve below T_c. The probability P_A of monomer A close to the B block is strongly affected by the length of the block B. The P_A of monomer A close to the end of the B block clearly decreases because of the non-adsorptive property of the B block. However, the existence of the B block does not affect the adsorption of monomer A close to the grafted monomer (x=0). The length of the rear block A affected by the B block is dependent on the length of the B block. The probability P_A of the rear block A decreases with an increase in m for the diblock copolymer A₁₀₀B_m.

Figure 4

The probability that each monomer A is in contact with the surface for the polymer A_nB_m with m=0, 50 and 200 near the critical adsorption temperature T=1.6. The slope of the solid line is −0.45. A full color version of this figure is available at Polymer Journal online.

The influence of the block length of the tail block B on the adsorption of copolymer A_nB_m is also studied. The mean surface-contact numbers <M_A> of the diblock copolymer A₁₀₀B_m are calculated for different values m and at different temperatures. We find that <M_A> is related not only to the temperature, T, but also to the length of the B block. As in the case of A_nB_n, the ratio , which describes the contact number reduction because of the B block, is also calculated. Figure 5 shows the dependence of f_<M> on the temperature, T, for the copolymer A₁₀₀B_m with different m values. At a very low temperature, the ratio f_<M> is almost constant with respect to m. As the temperature, T, increases, the ratio f_<M> rapidly decreases with an increase in m. There is a minimum of the ratio f_<M> just at the critical adsorption temperature, T_c. These results indicate that the tail block B influences the surface-contact number of monomer A for the diblock copolymer A_nB_m; however, it has no influence on the critical adsorption temperature, T_c.

Figure 5

Plots of the ratio f_<M> of the <M_A> of diblock copolymer A₁₀₀B_m to that of the homogeneous polymer A₁₀₀ at different temperatures, T, for different lengths of the B block, m.

The copolymer A_nB_m can be separated into two types by comparison of their surface attraction. If the attraction strength of monomer A is stronger than that of monomer B, we can set E_AS=−1 and E_BS=0 as the limitation, otherwise we set E_AS=0 and E_BS=−1. For the former case, our simulations show that the T_c of E_BS=0 is equal to that of E_BS=−1 corresponding to the homogenous polymer A_n. Therefore, we conclude that B block has no effect on the critical adsorption temperature, T_c, if E_BS>−1. Although we only study the case E_AS=−1 and E_BS=0, it in fact includes all E_BS>−1. For the other case with E_AS=0 and E_BS=−1 (that is, the limitation for the attraction of B is stronger than A), the situation differs because the adsorption of B takes place before that of A. This case is more complicated but deserves further study.

Conformational properties

We also studied the influence of the non-adsorbed B block on the conformation properties of the A block for the diblock copolymer chains A_nB_m. The dependence of the mean square end-to-end distance of block A <R_A²> on the temperature, T, is shown in Figure 6 for n=100 and m=10, 50, 100 and 500. The <R_A²> displays a minimum value near the CAP T_c=1.625, which is in agreement with the behavior of the homogeneous polymer.^17,19 Therefore, the place where <R_A²> is minimum is defined as the critical adsorption temperature for a finitely long polymer.¹⁹ At high temperatures, T>T_c, the <R_A²> changes little with the temperature but increases with an increase in the length of block B. At low temperatures, T<T_c, the <R_A²> is mainly determined by the temperature. We find that the critical temperature T_c(A_nB_m) for a finite long chain A_nB_m, where <R_A²> is a minimum, is dependent on the length of the A block, n and the length of the B block, m. The critical temperature T_c(A_nB_m) first decreases with an increase in m for a short B block. When m increases to a certain value (m=n), then the critical temperature T_c(A_nB_m) is roughly independent of m, as shown in the inset of Figure 6. These results clearly show that the B block influences the critical adsorption temperature of the A block of the diblock copolymer A_nB_m. In other words, the T_c(A_nB_m) of the finite copolymer A_nB_m is dependent on the length of the B block, although block B is inerted to the surface.

Figure 6

Plots of the mean square end-to-end distance <R_A²> of the A block versus the temperature, T, for the polymer A₁₀₀B_m with different lengths of the B block m. The inset shows the effect of the T_c(A₁₀₀B_m) of the diblock copolymer A₁₀₀B_m on the length of block B m.

It is known that the T_c(A_n) of finite long chain A_n is dependent on the length of the polymer.^{17, 18, 19} The dependence of T_c(A_nB_m) on the length of the A block is checked for copolymer A_nB_m. To this end, we choose A_nB_n as an example, and T_c(A_nB_n) is estimated from the minimum of <R_A²>. The dependence of <R_A²> on the temperature, T, is plotted in Figure 7 for both A_nB_n and A_n with n=100. Each curve has a minimum, and the temperature of the minimum is named as the critical adsorption temperature T_c(A_nB_n). Again, T_c(A_nB_n) is lower than that of T_c(A_n) because of the influence of the B block. We have calculated the difference ΔT_c between the two critical adsorption temperatures, which is defined as:

Figure 7

Plots of the mean square end-to-end distance <R_A²> versus temperature, T, for the homogeneous polymer A_n and for the A block of the diblock copolymer A_nB_n with n=100. The inset presents the critical temperature difference ΔT_c, ΔT_c=T_c(A_n)−T_c(A_nB_n) because of the B block.

We find that both T_c(A_n) and T_c(A_nB_n) increase with the length of the A block. However, the difference ΔT_c decreases with an increase in n, as shown in the inset of Figure 7. Our results indicate that the tail block B influences the location of the minimum of <R_A²> for the A block of A_nB_n for a finitely long polymer but has almost no influence on the location of the minimum of <R_A²> for an infinitely long polymer. Therefore, the influence of the B block is eliminated with the increase in the length of the A block, and ΔT_c tends to 0 for an infinitely long polymer. This result also explains that the CAP of the diblock copolymer A_nB_n is the same as that of homogeneous polymer A_n for an infinitely large n.

Asphericity parameter

In addition to the statistical size of the copolymer, the statistical instantaneous shape behavior of the copolymer A_nB_m near the critical adsorption temperature is investigated. The instantaneous polymer shape can be expressed by the mean asphericity parameter <A>, which is defined as

in a three-dimensional (3D) space.^17,31,32 Here, and () are the three eigenvalues of the radius of gyration tensor S, which is defined as

where the matrix s_i=col(x_i,y_i,z_i) represents the position of monomer i in a frame of reference with its origin at the center of mass.^31,32 is the transposed matrix of s_i. By this definition, we have (α, β=x, y, z). Specifically, S_xx, S_yy and S_zz are the three components of the mean-square radius of gyration along the x, y and z directions, respectively. The mean asphericity parameter <A> of the A block in A_nB_m is calculated at different temperatures. The relationship between <A> and the temperature, T, is presented in Figure 8 for A_nB_m with n=100. <A> does not change with T at high temperature T>T_c; however, it clearly increases below T_c and saturates at low temperatures. The values of <A> change from ~0.45 at high temperatures to 0.62 at low temperatures, indicating a transition from a 3D configuration to a two-dimensional (2D) configuration. At high temperatures, T>T_c, <A> increases with an increase in the length of the B block m, whereas at low temperature T<T_c, <A> is roughly independent of m. We have checked the influence of the B block on the instantaneous shape of the copolymer by defining a ratio f_<A> as

Figure 8

Plot of the mean asphericity parameter <A> of the A block versus the temperature, T, for A₁₀₀B_m with different B block lengths, m.

where is the asphericity parameter of the A block of A_nB_m and is that of A_n, respectively. The dependence of f_<A> on the temperature T is shown in Figure 9. At T=T_c, the ratio f_<A> is equal to 1, indicating that the length of the B block m has no influence on at T_c. This result is consistent with the asphericity parameter of the homogeneous polymer chain that is independent of chain length at CAP.¹⁷ At high temperatures, the ratio g_<A> is greater than 1. The movement of the tail block B drags the A block away from the surface and increases the size of the block A (Figure 7) as well as the asphericity parameter. At low temperatures, the ratio f_<A> is slightly less than 1. The movement of the tail block B again drags the A block away from the surface, indicated by the decrease in the adsorption probability with m as shown in Figure 4. This prevents the adsorption of tail monomers in the A block; thus, the size (Figure 7) and the asphericity parameter (Figure 9) decrease with the length of the B block. It is known that a 2D configuration has a larger asphericity parameter.

Figure 9

Plot of the ratio f_<A> between <A> of the diblock copolymer A_nB_n and that of the homogeneous polymer A_n at the temperature, T, for different B block lengths, m.

We have also investigated the adsorption of the copolymer A_nB_m with a stronger surface attraction of monomer B. In addition, we simulated the copolymer for a limitation case with E_A=0 and E_B=−1. Interestingly, we find that the critical adsorption temperature is the same as that of the homogeneous polymer when the length of the tail block m tends to be infinity. However, the dependence of the conformational properties on the non-adsorbed block is more complicated. Nevertheless, all of our results show that the critical adsorption of the diblock copolymer A_nB_m is determined by the block with stronger attraction.

Conclusions

Dynamic MC simulations are carried out for investigating the adsorption of a single flexible diblock copolymer chain A_nB_m with the head monomer A grafted to a flat surface. The surface is impenetrable by the copolymer through the adoption of a self-avoiding walk. This article considers a specific case with attractive surface interactions of monomer A and non-attractive monomer surface interactions of monomer B. The finite-size scaling law is adopted to determine T_c and the crossover exponent, φ. We obtain T_c=1.625 and φ=0.51 for the infinitely long copolymer A_nB_n. Our results show that the critical adsorption temperature and exponents of the diblock copolymer A_nB_n with a large n value are determined by the A block that has a stronger attraction. To investigate the effect of the B block on the finitely long copolymers, we compared the contact number of A_nB_n with that of homogeneous polymer A_n. We found that the non-adsorbed B block weakens the adsorption of the A block; however, the effective influence of the B block on <M_A> is independent of n at T_c, resulting in the same T_c and φ for both A_nB_n and A_n at large n. Simulations on the general copolymer A_nB_m give the same conclusion that the non-adsorbed B block does not influence the T_c of a long A_nB_m.

The non-adsorbed B block also influences the conformational properties of the end-grafted copolymer A_nB_m. At high temperature, the B block increases the size of the A block and the asphericity parameter. At low temperatures, the B block prevents the adsorption of tail monomers in the A block; thus, the size and the asphericity parameters decrease with the length of the B block. At CAP, the asphericity parameter <A> is independent of the B block, which is in agreement with the properties of homogeneous polymer. The temperature variation of size and shape shows a phase transition of the A block from a 3D configuration at high temperatures to a 2D configuration at low temperatures. However, the influence of block B dies away with an increase in the length of the A block.